Voting property restrictions were state by state, and their disappearance was a gradual process. Jackson wasn't so much of a turning point on this as is sometimes imagined. Suffrage among white adult men in many rural areas was nearly universal early on since the property requirements in most states were fairly low. Another thing to keep in mind is one of the main arguments in favor of property requirements was that it would keep the very wealthy from having too much power by buying votes of the very poor, so the politics of this weren't always what you'd expect from a modern perspective.
Loosening of property restrictions definite pre-date the Jackson Administration.
I have an ancestor who lived in Virginia for 30 years. He didn't own land, and he appears in almost no records. (He had two kinsmen with the same name, but I can definite rule out either the William married to Eleanor, or the William married to Jane, as my ancestor.) Outside of 3 people with his name routinely appearing in tax lists, almost the only proof of him being in Virginia in 1806 comes from a son who reported, in the 1880's, his birth there at that time.
Soon after his son's birth, he moved to Ohio, where he lived another 25 years. Again, he never owned land, but I know he was there because his first 3 records were on eligible voter lists in 1807, 1811, and 1815.
