I dunno, it sounded like just an alternative descriptor. Someone might say, “Let’s motor.” instead of “Let’s go,” or you might describe a fast walker as “really motoring along.” I didn’t sense that the OP was using it as a coy euphemism. He wasn’t saying it TO the person, just describing his leaving to us. It would have sounded weird to say “the guy had already walked off.”
And I’ll also give someone who works with disabled people the benefit of the doubt.
I suspect the benefactor has had an awesome caregiver in the past and knew exactly what he was doing when he said ‘keep the change’. Enjoy it, Homie.
[off topic]
Well, yeah, but I’d never tell a person not in a wheelchair to “walk this way” either, because I’ve seen too many cartoons*. I’d say “Follow me.” or maybe “Come this way.”
*The ones where the funny looking character says “Walk this way” and then walks off in a bizarre way, whereupon the main characters imitate his (it’s always a him) walk as they follow.
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Left Hand of Dorkness summed up my opinion perfectly, and eloquently too.
Money’s yours, dude.
“Keep the change” always means that the person to whom the money is being given should keep the change. It doesn’t mean “Hold on to the change until you give it to someone else, who is unnamed but you will be required to divine who it is.”
You should keep this $11 with absolutely no guilt whatsoever.
Unless EXPLICITLY prohibited by your employer, NEVER turn down a tip.
Young Frankenstein?
“Come this way” was the first thing that popped into my mind, too. Not everyone rolls, not everyone walks…but everyone comes! (Hopefully.)
There’s a difference, then, between the way things are in America, to the way they are here in NZ. “Keep the change” to the shopkeeper or service provider is the equivalent of the tipping custom, yes. But “keep the change” to someone clearly involved with a charitable organisation of some kind usually means “the rest is donation”, ie. to the charitable purpose.
In my case, with giving more than say a ticket-price on an item at a trading table run by the local church, I say “the rest is donation.” Lessens any confusion.
If the chap in the OP had said, “The change is for you,” that would have been clearer.
HeyHomie, were you in a uniform? If so then I’d have thought that the guy was giving you the money in your official capacity rather than to you as a person. Otherwise, while I don’t think you did wrong - see Silver Fire’s and OslerKnew’s comments - I think you would have done better to consider it a donation to the charity.
Ice Wolf he doesn’t work for a charity. It’s funded by tax dollars. Still I would expect a person I told to keep the change to keep it.
We have non-governmental organisations funded by government grants. “Group homes” here usually come under that description, so again – apologies for the national differences, here. But, with the other option being to give the remaining $11 into the general fund “from which we pay for the residents’ activities”, that might have been better than simply keeping the money. I agree with Quartz.
I just didn’t want you to think it was a charity, or I wouldn’t have mentioned you at all.
No worries, Harmonious Discord. Thanks for the info. 
“Keep the change” means keep the change, to me at least. Do what you want with it. In the situation in the OP, I read it as someone saying “I appreciate what you do for these people and for the world. I would like to help you out by buying their drinks, and I would like you to keep the change as a thank-you.”
In my day-to-day life, if I say “Keep the change,” it only means that I do not want the coins (usually a penny or two). Throw them away for all I care.
I work in retail, at a store with a specific non-tipping policy. When someone tips me, I donate it to the Special Olympics collection box we have at each register.
Joe
blink
I say “motored” for people moving at a higher-than-average rate of speed, regardless of their method of propulsion.
In the OP, I was reading “motored” more as a descriptor of velocity than as a method of transport. On rereading, it’s clear that the giver was in a wheelchair, but the first time through, I didn’t really register that. I just thought the OP meant the dude left in an expeditious fashion - i.e., before the OP had a chance to protest or discuss the cash with him.
/edit because I’m a dork and forgot to answer the OP’s question: I think the OP acted perfectly ethically and appropriately in those circumstances.
I would have kept the money as well. Here’s something to think about. What if the stranger was under the impression that you had been paying for the sodas out of your own pocket. That is, if he didn’t realize that these where residents (or at least that you where the care provider for the day) and that maybe you where just taking them out for the day for some other then it being your job?
As an employer for a day program for developmentally disabled adults, I don’t see your actions as unethical. FTR, I don’t have any policies against my employees accepting tips.
OTOH, if you happen to wear a uniform or a shirt with a company logo on it, I could see a such a policy being a good thing to protect the employee from being accused of pocketing money from a third party witness, and the implications that arise from it. But, it seems that wasn’t an issue in your OP.
If it was me…I would spent all $20 (sodas and/or snacks) and split it three ways, or four ways (if I was hungry or thirsty)…but that’s just me.