Depends on which parallel universe I was in.

Assuming the scenario took place in this world, I would be overjoyed to see a living
Rhamphorhynchus, and even more excited when I found out I could talk to him. I’d probably take him into the house and drive him crazy with questions about where he came from, how he got here, if there are others like, them, and if I could see them, too.

If I lived in a world where it was normal for LBT characters to appear on your doorstep, I’d probably be a lot more cautious. I’m pretty meek, and don’t like trouble, so I’d try to be polite to him; maybe ask him what he wanted (preferably without letting him inside). My actions thereafter would depend on his response. If all he wanted was food, I’d probably give it to him (assuming we had something he liked). If he was up to no good, I’d probably try to keep him from getting in the house. If worse came to worse, and he got inside the house and tried to attack me, I’d probably run and try to find something to defend myself with. I’d be most afraid of the damage his beak, teeth, and claws could cause (I imagine it would hurt to be hit by his wings as well), but there’s not a lot of space in our house for him to fly, and plenty of rooms I could lock myself in. I’d probably try to stun him (or at least hold him back) with a broom or other household object until I could trap him in a laundry basket or storage bin or something. After that...I don’t know. Call the cops? Animal control? John Hammond?

Depends on what my options were.
In either situation, he’d would have to watch out for my psychotic cat. Sasquatch would probably think Rinkus was something new to play with, and chaos would ensue.

P.S. I'm not great at identifying accents, but Jared, I'm pretty sure Rinkus has a Cockney (English) accent, not an Australian one.