Hi there. I think you're doing well with the timing. There's only some slight inconsistencies in the triplets during the middle section, especially when they are about to move into the 16th notes at 0:49. Try to maintain the triplet feel until it's time to play the 16th notes.
The last section: The timing for this section is quite good. The thing that is messing you up is that you're missing out 1 note at the end of each 16th note part. The picking should be constant.
What you do is miss the last one out.. and because your picking hand pauses, you resume the next note with the opposite stroke. This is confusing things for your picking hand.
Each time you move to a new note you should always be starting on a down stroke.. if you pick all the notes like the lesson then this will naturally occur
If you miss notes out though, it can mess up your picking pattern. Try it with one of the slower backing tracks and identify what I mean and you can experience this for yourself.
If you can eradicate that issue, then you'll be able to nail this lesson easily and you'll be ready for more picking work !