Controlling a Linear Actuator

There's no Schematics and scarce, questionable Specifications, and questionable compatibility,
on all of your "Specified Parts",
how do you expect anyone to figure-out how they work without personally
taking each item apart for internal inspection and testing to find-out how they are set-up to work ?

This looks like yet another "Chicken-Coop-Door" project.
( Do I win a prize for guessing the application ? )

This is exactly why I would never buy anything from someone who has
zero knowledge about the product that they are selling,
other than what the sticker on the bottom of the item claims.

If You can get all this stuff to work together like You imagined, then "more-power-to-ya",
but it would be 100% guesswork to even try to make a suggestion without
personally testing, and inspecting, the "specified" mystery-parts.

Here's my suggestions ..........
Start-out with a Power-Supply that can easily deliver twice the maximum possible Load.
Your Actuator claims a maximum of ~3-Amps, so get a 6-Amp Power-Supply, or larger.

Get a standard, mechanical, 24-Hour-Timer designed to plug into a standard Power-Outlet.

Use the Timer only to Power a DPDT-Relay, with a
Coil-Voltage rated the same as your local Wall-Outlet-Voltage.
The above Power-Supply will remain Powered 24/7,
and will not be Powered by the Timer.
( Unless You want to use 2-Timers, one set to ~1-Hour, and one set to ~15-Minutes )
( A cheap Timer will cost You more Money than the extra Cost on your Electric-Bill to run the
Power-Supply 24/7 for a year )

Wire the Relay for reversing the Power going to the Actuator.
Relay-Coil Powered = Close, Relay-Coil not Powered = Door Open.

Hopefully, the claimed non-adjustable "Limit-Switch" (there should be 2) will
safely stop the Actuator-Motor when it remains Powered-On,
and will not re-start the Motor until the Power-Polarity is reversed.

Good Luck ......