My experience with this is very limited, as my ex has only met one man that I dated. Personally, I am extremely cautious about introducing my children to anyone. The relationship has to be at certain level for that to happen, so, there is no reason for my ex to have that exposure unless the kids have.

First, does your ex know that your b/f is coming to town and spending time with your kids? Has your b/f spent time with your kids before? I made it a point to let my ex know this information prior to it happening. I didn't want him to feel caught off guard if the kids brought up the b/f (activities we did together like going to the park). I chose to handle it this way, because, this is how I would hope he would (he is remarried so the point it moot). Just give him a, "Hey, I want to let you know that X will be here this weekend. Just thought it was important you heard it from me and not second hand from the kids."

When the introduction did occur, we happened to be at my son's soccer game, so, it was neutral territory. My b/f went up, introduced himself to my ex and shook his hand as if he was meeting a friend of mine. No big deal and zero tension.

I think the tension will only be there if you, your b/f or your ex put it there.