As you progress through your musical journey, play with better players, and gain different experiences, you understand that pocket playing takes on an ever-increasing nuance. How picky do you want to be? If you play with top-tier players, they will certainly pick apart a bassist who does not lock.
It is required to be present and listen at a very high level of consciousness to what everyone around you is playing. Music is conversation.
Studying the role of the bass as it pertains to a style you wish to play means becoming an expert on the genre's components.
For example, if you want to play authentic blues or shuffle style, you do not push the front half of the downbeat. Listen to the Babalon Sisters by Steely Dan with Bernard Purdie Drums and Chuck Rainey Bass. If they sit any further back, they would be behind the beat. The relaxed approach makes that groove so freaking powerful and hard to play for many players. That approach is completely wrong for Van Halen, for example.
The definition of " in the groove" is, to some extent, a moving target and genre-dependent. You need to know which approach is appropriate and have the command to make those adjustments.
To the OP, regarding your videos, I would say to you, analyze (listen) where you play the downbeat and where the drummer hits the kick on beat one. I hear that you are on the front of the downbeat. With your full concentration, try not to be ahead, try to be one with where he is laying it down. The groove will get fatter instantly. Record every gig and see how your adjustments change the groove of the entire band. Bass holds a lot of power regarding the feel of the rhythm section. You should be talking to the drummer about how to approach the groove so he is as focused as you are.
This is the super-picky, rarified air that great players spend their time working on.
I agree with Bherman; practicing with a metronome is helpful. Try having it click on beats 2 and 4, which are the backbeat. That alone will help your internal clock develop.
Andrew Gouche, Bass... the kick and the bass can not lock any tighter... even if you don't dig the style of music, this is spectacular.