Who are the one accusing him? Random people on the internet. His career arc is pretty typical of a HOF'er. Great player that is productive into his mid 30's. That is really what separates great players from HOF'ers: longevity.
Those pictures that person used are misleading, that rookie card is from 1991, not 1994. The entire article is either written from ignorance or with a purpose to distort facts and hope people do not take the time to look them up.
There is no magical season where all of a sudden his numbers jump to insane levels. Look at Barry Bonds career, age 36 to 40 his numbers blow up to insane levels. He goes from one of the best players to ever play the game to video game god mode turned on numbers.
It seems like the article was written by somebody who had never followed Thome until his HoF induction.
Age 23: '94 - 20 HR in 321 AB, 6.23% of at-bats ended in HR
24: '95 - 25 HR in 452 AB, 5.53%
25: '96 - 38 HR in 404 AB, 7.52%
26: '97 - 40 HR in 496 AB, 8.06 %
27: '98 - 30 HR in 440 AB, 6.82%
28: '99 - 33 HR in 494 AB, 6.68%
29: '00 - 37 HR in 557 AB, 6.64%
30: '01 - 49 HR in 526 AB, 9.31%
31: '02 - 52 HR in 480 AB, 10.83%
32: '03 - 47 HR in 578 AB, 8.13%
33: '04 - 42 HR in 508 AB, 8.27%
35: '06 - 42 HR in 490 AB, 8.57% (first year as primary DH)
36: '07 - 35 HR in 432 AB, 8.10%
37: '08 - 35 HR in 503 AB, 6.76%
He became a part-time player after this.
As I said before, that baseball card was from when he was 19 or 20, so I would expect him to add a lot of mass between then and the prime of his career. His best seasons were '95-'98 and the '01-'02, so ages 24-31. Nothing out of the ordinary there.
Here's Thome in 1993, he turned 23 that August
Here he is in '96 right before he turned 26
Here is his baseball from 2000, so I assume it's a 1999 picture
Here he is in 2002
Looks like a pretty standard progression for a guy entering his prime and then his 30's
If you want to say Thome was probably on something because most guys were, I understand that cynical approach. You have been given every reason to think that way. However, there was no production spike or body transformation that would suggest PEDs. As I said before, the article is completely bogus.