Does your permanent duty commander have OPCON authority over you when TDY?

There is OPCON and ADCON. You may fall under the jurisdiction of the TDY Commander, but your regular unit command may very well have ADCON (administrative control) on you. I'll have to try and find the reg when I can get to my computer since I'm on my phone right now.

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Yes, the permanent commander retains OPCON until that OPCON is delegated (in writing) to another commander.
That delegation of OPCON process is intended for BNs and BDEs within a COCOM deployed to a Theater of Operations, not something that happens for individual TDY.
Most common reasons for TDY are schools, non-school training, conferences and boards.
The local commander or school commandant has general military authority, but the Soldier's commander still has command and UCMJ authority.
That's why in serious incidents involving UCMJ, the Soldier is merely dismissed form the course, while the unit commander is responsible for any required UCMJ action for the incident.
The purpose of the TDY is that Soldier's primary responsibility for the duration.
Primary, but not sole responsibility. That said, there should be some expectation management:
If the Soldier is at a school or conference that is skipping PT and conducting class from 0800 to 1530 with 90 minute lunch breaks, yes the Soldier can be expected to action something for their commander same day/next day.
if that Soldier is in Ranger school with access to their phone for 8 hours every 2 weeks, the commander can reasonably expect to wait until graduation.

And the commander retains the authority to recall that Soldier early from TDY, even a school, same as recall from leave.