We never had the exclusivity conversation, I'm pretty sure that's just on TOWIE!
Nah! I always insist on the exclusivity conversation
around the time of DTD (ideally before but doesn't usually happen...
)
With the guy I am kind of seeing at the moment, I've thrown all rule books out of the window but it seems to be working so far..
First date (2 weeks ago) was cinema (usually a huge no-no but it worked for us!) with drinks after. I invited him back to mine for "coffee", hoping for a snog but he didn't take the bait, drank his coffee and left 
Second date was lying on his bed watching movies...and then DTD, obvs. 
Third date we did a bit more properly - dinner and back to mine.
Fourth date is planned for this weekend, and hopefully he'll stay over.
I knew before our first date that he wasn't talking to anyone else as I teased him about getting me mixed up with someone else and he confessed he was only talking to me. We chatted again on our third date and agreed that we are only seeing each other.
It's definitely not a "relationship" yet, though we are not seeing anyone else and plan to spend all the free time we have together (but this is mainly because we don't have much that coincides...)
OP, what about a "relationship" is going to make you feel more secure? More messages? Some kind of statement of commitment? You might want to use this time with him being away to think about what specifically is going to reassure you and then you can think about addressing that.