From the section on opportunity attacks:

You can make an opportunity attack when a hostile creature that you can see moves out of your reach. To make the opportunity attack, you use your reaction to make one melee attack against the provoking creature. The attack interrupts the provoking creature’s movement, occurring right before the creature leaves your reach.

"Creature moves", "provoking creature", and "interrupts the provoking creature's movement", all support the position that the intent of opportunity attacks is to react to another creature's movement, not your own. This is further clarified in the subsequent paragraph to mean "voluntary movement".

If the intent of Polearm Master was to subvert the general rule with a specific one, it would be clearly stated, as in "This is an exception to the general rule on opportunity attacks, in that it does not require movement on the part of the target". The phrases "enters your reach" and "moves into your reach" are--barring any explicit wording to the contrary, pretty clearly synonymous. A relative movement interpretation does not match anything else in the book, unless it is clearly described as such.

In short, "Enter" is an active verb, and had Polearm Mastery" been intended to break of the general rule, it would certainly have been pointed out by the designers in errata, interviews, tweets or Sage Advice.

In the absence of anything like that, the general rule interpretation should apply.

To solidly support this, user Korvin Starmast has kindly supplied definitive clarification:

Sage Advice Compendium, page 8:

Does Polearm Master let me make an opportunity attack against a target that is being forced to approach me? A creature doesn’t provoke an opportunity attack if it is moved without the use of its movement, its action, or its reaction"

Yes

As you have mentioned, Tunnel Fighter specifically mentions that it requires more than 5 feet of movement to trigger. I see no reason that we would disregard that statement. However the PHB entry for AoO would seem to imply logically that, in fact, the quarterstaff attack would have happened just after the creature enters your reach:

You can make an opportunity attack when a hostile creature that you can see moves out of your reach. To make the opportunity attack, you use your reaction to make one melee attack against the provoking creature. The attack occurs right before the creature leaves your reach.

emphasis mine

Even though this example is in the standard AoO case of an enemy leaving your reach, there seems to be no reason to believe that the reverse would also be true and that the enemy would be less than 5 feet away from you when you AoO with your quarterstaff.

This means then that the conditions for your Tunnel Fighter ability are indeed triggered, and that you can then attempt to make that attack as well. There do not appear to be any general or specific rules that would prohibit multiple things happening based on multiple triggers and your character definitely has the actions to perform it so there seems to be nothing that would prevent this from being perfectly legal.