As Tim said, this is a puzzle. As I was reading your description I had the exact same thought he did regarding air trapped under the agitator skirt, but the fact that it stops agitating and resumes filling is a real head scratcher. The logical place to look here would seem to be the air tube or the fill level selector switch, but you say you've already looked there. At this point all I can think of would be to mix some dish soap and water together to form a thin leak check solution, then either brush it or spray it on the air tube and the air tube end where it connects to the fill level selector switch. If you have even the tiniest of leaks it will blow bubbles with the solution. The problem you're describing really does sound like a leaking air tube, but a leaking diaphragm in the selector switch will cause the same symptoms. As you already know, as the tub fills with water that water flows into the lower end of the air tube and pushes the air in the tube up against the diaphragm. As the tub fills the water in the tube rises correspondingly until the pressure on the diaphragm is high enough activate the switch. Once that happens the fill stops and the agitation begins. The only way the machine will interrupt the agitation and resume filling is if that pressure has bled off somehow thereby allowing that switch to open. The fact that it then fills to a higher level would seem to be further proof of this, so I think I'd continue to focus my efforts there for a bit longer.

One thing to keep in mind - after you initially fill the tub to the desired level, either take note of or mark the water level on the agitator barrel. For a water leak to open the contacts in the selector switch you'd have to loose enough to see it drop away from your mark on the barrel. But a loss of air pressure will trip that switch with no discernible drop in water level.

Hi, Its the new air-dome hose or the new tubing itself.

As I think I said before, Quality Control on replacement parts 20+ years after the fact is not close to the quality of the parts that  the appliance was originally built with. I have also found out the hard way not to replace parts that are not bad when restoring an appliance.

Instead I replace parts that are worn or parts that normally do wear out and cause problems, this is where experience in the appliance repair business is so important, because I can look at an appliance and based on model, age, usage it has received etc and give you a pretty good guess as to what should be replaced to keep it functioning reliably.