We were in Arillas in May and the taverna we ate in - The Brouklis - was extremely popular, with all the tables being full every evening we were there.
We did notice that some other people pre-booked tables to make sure they had one at a certain time but, as we weren't that bothered about eating at a particular time, we would wander down the road to have a drink at one of the bars if we saw there were no empty tables. Then, 45 minutes or so later, we went back and usually found some of the tables had freed up by then.
So, if you want to be sure of a table at a specific time, it might be wiser to check with the taverna to see whether they want you to book beforehand. This is especially true if you want to visit some of the very popular places, like Taverna Agni for example, where, in the height of the season, you may need to give two or three days' notice.