This seems like a reasonable place for the topic, but the short answer is, no, you can’t integrate that particular device to SmartThings in any meaningful way.
That said, you don’t need to. You can assign a virtual timer to any button on any device that works with SmartThings. So just do it that way. 
http://thingsthataresmart.wiki/index.php?title=How_to_create_a_virtual_timer_for_a_light
Pick a SmartThings-compatible button device that you like the looks of, or use a Wi-Fi phone on the wall:
Then assign a virtual timer to each of the buttons and you can have each one go for whatever specific countdown time you want.
You will need one additional device controlling the actual load to whatever it is that you are setting the timer for, the button device is essentially just the remote with the different times stored for it.
The Nexia one touch lets you put a text label on each of the buttons.
Or there’s a remotec with eight different buttons that might work.
But again, see the FAQ: there are a lot of different options.