There is no hard and fast dividing line. And, there were some years that went against the custom of the times. For example, Andrew Jackson hand-picked Martin Van Buren as his running mate in 1832.
But in general, Nineteenth Century presidential candidates had little or no involvement with the VP selection. The presidential candidate was seldom if ever at the convention, and the telegraph wasn’t a completely practical way to solicit his input.
The telephone moved matters a little; by the late 1800’s/early 1900’s the presidential candidate would usually be consulted, and might veto particular candidates. But, this would not be a one-man show; party leaders at the convention would still be involved and the nomination sometimes went to a convention floor fight. For example, the Republican Convention of 1920 nominated Calvin Coolidge even though Harding and most party leaders preferred Irvine Lenroot.
Franklin Roosevelt took a more active role by virtually forcing the 1940 Democratic Convention to nominate Henry Wallace. (Roosevelt would have declined to run otherwise.) But party leaders didn’t like Wallace, and they in turn had enough pull to force FDR to back down and let the convention nominate Harry Truman (after a furious floor fight) in 1944.
By 1956, Stevenson’s allowal of open balloting for VP was already something of an anachronism. More and more, the presidential candidate (usually known in advance of the convention) would pick the candidate, and the convention would rubber-stamp it.
The final transition occurred in 1972-76. In 1972 George McGovern had to fight a contested convention, and foolishly deferred his VP selection until late at night during Convention Week, after he won the nomination. He and his aides picked Thomas Eagleton in haste, leading to a double disaster. First, the surprised convention delegates rebelled, forcing the convention through a multi-hour ballot which delayed McGovern’s acceptance speech until three in the morning. Second, Eagleton turned out to have serious mental health issues which rendered him inappropriate as a potential President.
In 1976 Jimmy Carter made sure not to repeat this mistake, initiating a careful VP vetting process starting in the weeks before the convention and announcing his choice (Walter Mondale) well before the rubber-stamp balloting. All candidates of both parties have followed his example ever since.