A man invites to himself, go or not?
I think you misunderstood him. Maybe he just wants to have a good time with you over tea. In general, listen to your heart. If you really like him, then why not? If in doubt, then you should wait, or even stop communicating altogether. If you are a straightforward girl, ask him straight!
It is summer now. There are many places for dating. Let him offer to meet somewhere.
If he's so dumb and doesn't offer to see you, offer to take you to a mall to help you choose a dress. Well, or what thing do you need. At the same time, spin it up so that it feeds you. If he feeds, it means not a miser and not a rogue.
Or first, invite him to your home to introduce him to his girlfriends or to his sister / brother (but not to his parents!). That is, to talk without sex. And then in the mall.
Are you sure you understood him correctly? Better to ask directly, at the same time you will find out how decisive he is. And you should not ignore, maybe he was preparing for this for a long time, and suddenly ... At the same time, ask yourself why he is to you.
If a man invites you to visit him on a second date, then it is clear why. If you are not ready for this, then just say that "you will have to wait, dear". Even if you pretend that you did not understand, ignore, you will be re-invited, or even if there is a second date, then another invitation will follow, which you cannot miss. Having heard your answer in 99,9 percentages, I can say that you will not see this gentleman again. If a person only needs to waste his time from you and he is unlikely to have money, a couple of dates is the maximum. Much faster he will be able to get it from other, more compliant candidates. If a person is interested in you, then this will not stop him and he will wait.
If you feel that you are not yet ready to move on to the next stage, then it is better to tell him that you have a lot of urgent matters, and you cannot come to visit him for some reason. Just tell him what the next time, and when exactly, then you yourself tell him about it. It is better not to ignore, otherwise the man may think that you do not want any continuation with him at all. Although there are different men. You can also talk to him about the fact that you are not ready, that you need more time. I think if you talk to him first, he will understand and will wait as long as necessary.
Make it clear that it's early, explain that you're not ready. He probably thinks that he is doing the right thing.