"Give me a plain cup, I'll somehow cover it and then I'll put it in," Thiem complained. "You guys are crazy about anti-doping and then you want to carry the Red Bull can out and you guys fill it in a plain cup.
"What the heck is this? Bring me a plain cup please and I'll fill it in."
Thiem eventually got his wish. An official brought out a can of Red Bull then tried to cover it with a towel as the right-hander poured it into a plain cup.
Thiem addressed the incident after his straight sets win, saying he understood the Red Bull can couldn't be seen on court. He described the situation as a "little bit awkward" and defended himself for wanting to see first-hand what was being poured into his cup.
"They wanted to go out with the open can and fill it in a plain cup without me observing it. That's what p***ed me off a little bit because the anti-doping rules are so strict," Thiem said in his post-match press conference.
"I don't want to lose the can out of my sight.
"In general, they are so strict rules these days, and they propose me to fill the can in a plain cup without me observing it.
"That p***ed me off a little bit."
Thiem will play 2014 US Open champion Marin Cilic in round three.
DEMON SURGES ONWARDS
Elsewhere, Vasek Pospisil knocked fellow Canadian Milos Raonic out of the major with a four-set win in their second-round clash while Andrey Rublev advanced to the third round with a 6-2 6-4 7-7 win over Frenchman Gregoire Barrere.
Aussie Alex de Minaur powered on, defeating 2013 US Open semi-finalist Richard Gasquet in four sets after countryman Jordan Thompson also won through to round three after disposing of Egor Gerasimov yesterday.