It would've been around 2017, maybe 2018, but unfortunately the only source for finding out which sets the autographed cards were released in has been Cardboard Connection.
Here's what we have so far from that 2013 game:
1 Dylan Cease = 2017 Bowman Chrome, SN199
5 Michael Gettys = 2015 Bowman, SN200
6 Nick Gordon = 2014 Bowman Draft, SN199
7 Foster Griffin = 2014 Bowman Draft, SN199
8 Grant Holmes = 2014 Bowman Chrome, SN225
9 Michael Kopech = 2017 Bowman Chrome, SN199
15 Carson Sands = 2015 Bowman, SN200
16 Touki Toussaint = 2015 Bowman, SN200
17 Chase Vallot = 2015 Bowman, SN200
18 Alex Verdugo = 2015 Bowman, SN200
It's also possible it was released much later. For example, Luken Baker was in the 2014 game but his autograph was in 2022 Bowman.
* Ed * L8 * Cards in my personal Collection are unavailable *