Huh - that was a "difficult" one !
Are you new into waveboards ?
Then it is very likely not the board but you, who has to forget ALL about your old TT habits...
The power and driving point is your FRONT foot on a surfboard, not the back foot like on a TT.
If you ride like a TT, you WILL experience the tail popping out all the time, and the board will feel "bouncy".
If you are a bit more experienced into waveboards, it is more tricky...
As you ask if your board is too "narrow" ?
The narrower the more grip the board has - wide boards will pop out of the water much easier.
Too small fins and too wide boards might also make the board "pop out" yes.
I have never experienced any board popping out though, only if TOO big fins, it will begin to feel "odd" and bounce more...
Just the opposite as "Outside" says, eventhough he is correct in theory yes.
But just like he says - what is your "experience" level, and what precise dimensions (or name) are your board and fins and your weight ?