My kids can see my texts on their devices. How do I change this?

If you have different Apple IDs then NOTHING is shared across devices. So you clearly do not have a different Apple ID from your children’s.

To check: On each iPhone tap Settings and tap on the name at the top of the screen. The next page will show the Apple ID that phone is logged in to. On that same page at the bottom all of the devices sharing that Apple ID will be listed.

Apple IDs are personal; they shouldn’t be shared any more than you would share a toothbrush. If you share an Apple ID with someone else many bad things will happen. Each user should have their own Apple ID, then you can create Family Sharing→What is Family Sharing? - Apple Support. That way you can share what you want to share and not share what you don’t want to share.

It is OK to share an Apple ID among devices used by one person, such as an iPhone, an iPad and a Mac; in fact, it is a very useful thing to do. But not between devices used by different people.

Here is Apple’s FAQ: https://appleid.apple.com/faq/#!&page=faq. See the 4th bullet item.

This is because you are sharing your Apple ID with your kids. Each child should have their own unique Apple ID, then you set them up with Sharing Sharing and use Parental Controls if they are underage.

This link explains Family Sharing --> Family Sharing - Apple

This link explains Parental Controls --> Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support

This link explains how to set up each child with their own Apple ID --> Help your child set up an iPhone, iPad, or iPod touch - Apple Support

back out after logging out to the opening page of Settings and there should be a prompt to create an Apple ID or to log in to one→Sign in with your Apple ID - Apple Support