Did puritans preach from tubs?

Factual Questions
1

Several Royalist broadsides (published songs) accuse the Puritans of preaching from a ‘tub’.

What does this exactly mean? Did they take baths and preach at the same time?

“And teach a Lecture out of a Tub,” --Protecting Brewer, from Rump Songs, 1662

“Cursing from his sweating tub the Cavaliers to Beelzebub” (from Old Song on Oliver’s Court)

“Some for a church, and some a tub, and some for both together;
And some, perhaps the greater part, have no regard for either.”

–tale of the Cobbler and the Vicar of Bray

2

Tub preachers in 17th century England street preachers without a formal religious education, usually dissenters and non-conformists. They were called tub preachers because they used an upside down tub as a lectern.

3

Egbert van Heemskerk’s The Quaker Meeting gives a good idea of what was meant.

But whether anyone ever actually did preach from one is another matter.

4

So they didn’t live in tubs? I knew they weren’t that cynical!