asmith Have you seen these notifications? Or do you just hear them from his phone? Have you told him that you noticed it?
Is it possible that he just gets notifications so frequently that some of them really do coincide with your texts?
If you're suspicious of your husband and you haven't told him about it and you have a way to record video that doesn't involve your phone, I have an idea for you. This is going to seem kind of elaborate, but it should make sense as a way to catch this happening without permitting any accusation that you knew when he would get a legitimate notification from someone else (e.g. "maybe she knew that so-and-so texts him at that time").
With a separate camera, you begin a video in another room while he's doing something that makes you confident he's going to stay in one place for a while and predict for the camera, "My husband will have a notification coming into his phone in about one minute, and then another one about one minute after the first time he asks me a question." (It doesn't have to be a question; it could be a proper noun or a laugh or something else that doesn't happen too frequently; but I would tend to go with a question.) Then you can enter the area where he is and position your camera in a place that sees both of you and that you can casually approach to show your phone to it.
Then when the first minute is almost up, you send a text to a friend. (Someone to whom you've already sent a message that you think your husband was notified about. Maybe it's a male friend. Have it planned out ahead of time in case he's able to see what the message says. He may be on the lookout for out-of-the-ordinary messages and if he sees one he might turn off his notifications.) Presuming that a notification comes into his phone at about the time you said it would, you have an ordinary conversation with him. Don't say anything that's going to prompt him to leave. About 30 seconds after he asks you a question for the first time, grab your phone, compose a text message, walk over and display your phone's screen to the camera, and send the message. Provided that he gets a notification, and provided that he wasn't getting notifications very frequently over this period of time, you have pretty good evidence to support your suspicion. If it didn't take very long for him to ask you a question, you may want to keep the camera running to show how seldom he gets notifications over a substantial period of time.
If you feel safe around him and you want to start something, you could ask him whether he wants to see a magic trick. You tell him that you can throw your voice. You're a techno-ventriloquist. Then you send a text message to someone ("Help me" possibly being a strong candidate), point to his phone, and behold his response when it goes off. Unless he's reading this comment, he'll be very confused about how to play it and he'll be trying to verify the implications on-the-fly, and he'll probably start saying something like, "Gee, how did you do that?", thinking that dumbfoundedness might be his way out of the corner. Then you tell him that's not the best part of the trick and you ask to see his phone. Someone who genuinely thinks you were playing a trick on him and isn't spying on your phone would hand the phone over. But he won't do that because it will be occurring to him that this was a ploy to catch him in his spying. He will at the very least show reluctance, which a genuine person in this situation would not do. (I don't know whether it would be worth trying to get him to open the phone because the notifications might be programmed to disappear. But if he does and you can see the previous notifications of your texts to other people, displaying it for the hidden camera might be a good thing to do.)
Then you grab your hidden camera on your way out of the house, start driving away, and in a safe location pull over and show this comment to the (still recording) video camera to prove that you expected him to exhibit that reluctance. Make sure you show evidence of the last text message you sent, too.
If all of this happens I would only let him try to explain himself over the phone, on a call that you're recording.