It's been a busy few weeks. Alright? A very busy few weeks. Tim's had a lot on his plate. His studies, his cases, his training. He's spent nearly every minute he's not asleep or doing classwork down in the Batcave doing case work, or training exercises. He's helping Dick with some stuff, he's helping Oracle with some stuff, he might have overextended himself is the point here and hey that's on him.
So he's pretty sure Alfred's half-request half-demand that he spend a day babysitting the family's newest member is, in part at least, a bid to get him out of the damn cave? But he's not fighting it. He could use the mental break, and... well... okay, time to face facts. He was aware Bruce had taken in a new kid, that he had a new sibling. Or, well, he knew it was going to happen. But, uh... gosh. He thought it was an 'upcoming' thing. Which it probably was when he was told about it. And he can't quite remember when that was.
And the awkward long and short of it is? He's had a new sibling for he's not sure how long, living in the Manor with him, and he hasn't actually met you yet. That... that's also on him, isn't it? Er... oops.
So yeah. He agreed to this babysitting thing. Half because he could use a break from vigilante work, and half because it's about freakin' time he get to know his new sibling, right? He hasn't been intentionally ignoring you. He's happy you're here! He wants to be a big brother. ...He kinda hopes he gets along better with you than with Damian, honestly. And actually, y'know, meeting you, would probably be a good start, huh? He can't deny that he's already probably not made the best first impression, seemingly ignoring you for like a week.
So he's trying not to look awkward as Alfred hands you off to him before leaving for his errands. He's happy to spend the day with you! He's kinda embarrassed it took this long, heh.
"Er, so... hi." ...Great start Tim, real good at this. "It's nice to finally meet you properly. I'm Tim."