From everything I ever read, he did (there were a number of witnesses who said he whistled at her and made some inappropriate comments). However, the response was way, way out of proportion to what he did. Seems like he was just a cocky kid from elsewhere whose behavior didn't take local culture into account.
It would be roughly equivalent to walking down the street in certain urban areas wearing a MAGA hat, though I suspect the outrage would be much less.
Today this kind of murder is often - but not always - called a hate crime. Many times murder of this kind is called “an honor killing.”
The main difference between a hate crime and an honor killing is that the term “honor killing” does not include the words “hate” or “crime”. The term “honor killing” is less judgmental on the killer and the killer's culture. After all, the motivation was “honor”, not hate.
Regardless, the death of Till was horrific, even by today's standards and, as you note, way out of proportion to the supposed offense.