Confused Newbie in DDLG Play

So here's my story and I need some feedback on whether I'm being an asshole or not. My husband is overseas right now, so I've been chatting with this guy who's into DDLG stuff online. He lives nearby and we finally met up last week after talking for a while. I was super nervous but also kinda excited. We decided to start off light with some age-play at his place, just watching movies in bed, me as the little one. It went pretty well actually, he’s really good at making you feel like a kid again. I mean not too much stuff, just calling me 'sweetie' and such. The tricky part is that it felt so natural to get into the roleplay mode. We kind of just went with it, him as the dad figure and me as his little girl, but still adults the whole time, don’t worry about that side of things. There was this one moment where he started to get a bit strict with me, like if I made a mistake during play or something. He said stuff like 'time-out' and would pull out this little notebook for me to write lines in it as punishment. I have to admit, part of me really liked how authoritative he was being, felt good somehow to be treated that way. But the other half of my brain was thinking if I'm being too submissive or something. It’s hard because we’re just starting out and still figuring everything out together. Afterwards, we talked about it. He said he enjoyed how responsive I was but also noticed I got a bit tense when he started disciplining me more seriously. We both agreed to take things slow and work on understanding each other’s limits better before moving forward. So there you have it. Am I overthinking this or am I already going down the wrong path? Any advice from anyone who's been in a similar situation would be great! Thanks.