I have searched the pediatric literature using every combination of words I could think of, and could find nothing recent (this century) about this.
Most of the papers on belching were either associated with GERD (gastroesophageal reflux) or the willful swallowing of air (called Aerophagia) that is considered more of a psychological disorder in older children and adults.
So what follows is, unfortunately, opinion.
Can sucking thumbs lead to burping?
Not likely. But
Can sucking fist lead to burping?
Sure. A fist isn't really mouth saped and sucking on it probably means there is a bit of air sucked in (you'd hear a little slurpy sound), and infants especially (yours is a baby) do swallow when there is air in the pharynx that could be swallowed. So fist sucking could be responsible for the second belch.
However, if this were the case, it would happen every time the baby sucked on his hand, not only after feeding. If your baby sucks on his hand at other times as well as after feeding but doesn't experience discomfort then, it's probably due to the air ingested with food.
Interestingly, looking up how to properly burp your baby is not particularly helpful either. It doesn't mention how long after settling (or that first burp) that a baby might still need to be burped.
So the question of your proper burping of the baby is unsettled.
Practical advice: You're probably burping your baby just fine. He may or may not be sucking in air and swallowing it while fist sucking. But he needs to suck his fist to self soothe, so please let him do it. If he gets fussy every time, burp him. Eventually they get better about not swallowing air with sucking.
If it only happens with feeds, plan to re-burp the baby maybe 5 minutes after your initial burping (before he experiences discomfort) if the baby is not sleeping. Alternately, if you hold the baby upright after feeding, this might help cut down on the fussiness/burping.
You might want to mention this to your primary health provider during your next visit. This might be a sign of GERD, though spitting up is much more likely associated with GERD than excess belching.