That is really up to you. You are the only one who knows how you feel about that.
In his eyes, he may see it as fair. He paid for the first date and thereby he may believe that you should pay for the next.
You have had a particular experience in dating where guys have normally paid for the first few dates before you pitch in.
You have now met a guy who is not like that.
It is up to you to determine whether you are okay with that or not.
If he is taking a while to respond to messages, it may be due to what he told you about his fear of being too overbearing.
He did tell you that he has been told by girls in the past that he is too attentive.
Even though he has now been out on a date with you, he may still be exercising a measure of caution when it comes to communication, so as to avoid repeating past mistakes.