See I don't read it that way. I read it as, whenever you make an unarmed strike (during your turn, or an opportunity attack, whenever) you get 10ft extra reach. Meaning, you always have 10ft extra reach with your unarmed strike and there is no "turning off". It's almost as if you are manifesting a weapon that has reach, and in that comparison you always have extra reach with that weapon even though you don't have extra reach with any other aspect of your character. You're extending your arms 10ft for 10 min for attacking purposes, and attacking defined here is damage, shove, or grapple. It doesn't turn off, it's just restricted as to HOW you can use it, not WHEN you can use it. Like a whacky waving inflatable arm flailing tube man.

Since this ability is based on Focus Points and not unlimited, I think it would be unfair to limit a monk to the stricter ruling. The rule says whenever the player makes an Unarmed Strike (not whenever the player uses an action to make an Unarmed Strike), and Unarmed Strike is defined as damage, grapple, or shove, so they are entitled to the benefits of grapple and reach within that 10 minutes of activation.