Don't know what cats are telling me

Our resident cat is a 1 year old neutered male(Tink) and we adopted a male kitten(Spooky). Not sure of age, maybe 8-10 weeks. We seperated new kitten, rubbed each with a towel, ect...all the suggested things. They play under the doors with each other. Tink uses paws with no claws, he does bite new kitten but it doesn't appear to be hard. Tink yowls for kitten if he isn't at the door. This has go on for a week.
So today we let them meet face to face. The kitten zooms through the house with Tink right behind him. Tink will trip him, hold him down and bite him, not hard but enough to hold kitten down. This makes kitten VERY angry!! Tink let's him go, and they are off again. New kitten will also jump on Tink. This went on for the whole 15 min they were together.
So my questions are: Why is Tink doing this?, Is he trying to hurt kitten?, Should I keep them seperate longer?, How long will this go on?
Any help will be greatly appreciated. Thank you, Tink and Spooky's mom.

I don't think you need to separate them. The older one is just teaching the younger who is boss in the house. Its natural and unless they really are physically fighting (you will know it) leave them to settle it between them.

I suggest you either put some dry food on the floor and invite both to come in together or get a toy and play with them both at the same time. All my older cats had to teach the younger kittens who was boss.

Thank you, I can relax now. I tried the toy and it helped calm things down. Thank you again.

I've added 3 cats over the last couple of years.. Hopefully successfully. Anyway, I usually supervise them together for the first couple of weeks just to be safe. If anyone started getting too aggressive or hissy I would separate them for a bit, just to let everyone calm down.

My Kitty was doing the same thing with Claw, the kitten. I posted on here and have been assured it is normal behavior. My worry was that Claw is so much smaller than Kitty but, I never see bite marks or scratch marks. I am assuming that Kitty is indeed just letting Claw know who was here first and who is in charge. Good luck with them.

Some great advice here! When the girls all moved in, they were acclimated to one another, having grown up together. However, when Mimi and Polly were spayed, Muffin HATED them! The growling and fighting went on for almost two weeks, until I finally won them over with tasty wet food and a toy they had to share. It took a few days for them to get over their fighting, but things returned to normal with a little time.

Thank ya'll for all the advice. Spooky is learning who the boss is, so Tink spends more and more time playing rather than showing dominance. They even take naps together. They have become fast friend. Thanks again.