Op, you are recently out of a marriage where you were unhappy, and having now found someone who makes you happy the last thing you want to hear from people is that what you're doing is wrong.
Truth is that it's normal to feel something when your partner moves on, more so if you were the one who ended it, because on a weird level, if you ended it then his feelings hadn't changed, and his moving on is an indicator that they have. Added to that it's difficult to imagine another woman playing a parenting role in your dc's lives, something which is likely if they stay together, and furthermore the feelings of another woman being the mother to your dc's future siblings.
But ultimately these were the choices you made when you ended the relationship. The choice to let him go, and the choice to potentially let him be free to have children with someone else. You can't be jealous now that he is moving on in a way which you would surely have wanted given you ended the relationship?
Wrt your introduction of your bf to your children, people will comment based on their own opinions of what they feel is right or wrong. Truth is that there's no set answer really, but what I would say is, introducing a new partner to the children very early on carries significant risks, because when you are in the first throws of romance you are living for the moment, and after four months you really have no idea whether this is a relationship which will work or not, and if it doesn't then the children stand to get hurt again.
My ds was introduced to my dp early on not because that was what I wanted but because my xh threatened that if I didn't tell ds I was seeing someone then he would, so he left me no choice. I had planned their introduction months down the line, actually I hadn't planned it at all and we had planned to spend time together which coincided with ds not being there months down the line iyswim. I was lucky, my ds and dp got on extremely well from the outset, and just over two years on we are engaged although we don't live together as yet. However, at that beginning stage there were absolutely no guarantees, and had the relationship not worked out my ds would have been hurt by being introduced to someone else who he had become attached to and then having to break that attachment iyswim.
What's done is done now and you can't un-introduce the dc, but I would certainly ensure that there is time for just the three of you to spend together without your bf, especially as they're still so young, and also if things don't work out with your bf it will be easier to fade him away out of the dc's lives if he doesn't spend all your time together, iyswim.
Obviously that doesn't have to be the plan for ever, but this is a new relationship for all of you, and while you can take things as fast as you like the dc are young and live for the moment. They won't be seeing into the future right now.
My xh started seeing someone at around the same time as me and introduced her slightly later on. But she has a dd, and within eighteen months they were engaged and she is now pregnant. My ds has found that transition much, much harder because the moving on hasn't just included another woman but another child and now a half sibling (ds has been an only child for nearly thirteen years). In the beginning he seemed fine with their relationship but as time has gone on he's become more unsure, and as he enters teenage years I am aware that he could still have reservations about mine and dp's relationship e.g. when we get to the point of living together because children take these things on as they're faced with them. So just because the dc are happy now don't become complacent and take it as read that this is the future