As a few people have mentioned, you are probably using a rest stroke - meaning your finger plucks the A string and then hits the E string, causing a low frequency thump. If you don't like that sound (it's a thing, but not necessarily a bad thing), you can land your finger on your thumb as you mentioned (I use that technique sometimes). Or you can use a free stroke, where the finger travels over the E string after plucking the A string.
I used to play exclusively with rest strokes, as that gives the biggest and most muscular sound and a bit of free muting. But free stroke is nice for getting more delicate and singing tones.