The Frenchman is one of the few players who can boast of a ideal record on grass against eight-time Wimbledon champion Federer.
Federer, now ranked World No. 3, is aiming to capture his 10th tournament win in Westphalia.
Millman had beaten Federer at the US Open past year, yet the 20-time grand slam champion - bidding for a 10th title in Halle - controlled their clash on Tuesday.
Federer first appeared in Halle in 2000 and has gone on to play the tournament 15 times, although he was beaten by Croatia's Borna Coric in the final past year.
Australian Millman dug in early on and reached a tie-break without facing a single break point, instead putting Federer under a little pressure in front of a nervy crowd.
The two have met only once on the surface, a gruelling battle at Wimbledon in 2011, which Tsonga won after clawing back a two-set deficit. "I love to play at this venue, so I am going into the tournament with a very good feeling".
The foot-tennis-rally continued for some time with both players showing off a skill set that could just about rival that of their national football team. Federer has a hotel room with a view overlooking the Noventi Open's Court 1.
Tsonga, 34, missed seven months of last season due to knee surgery, but has shown solid form this month upon his return to grass court tennis for the first time since 2017. "I feel fresh, rested and ready for the grass season now". I think I had a clear game plan, I knew that it was going to be more hard for him to dominate the baseline. "It's always extremely tough to play against John. He always gives 100 per cent on court and it will be a real test, but that is perhaps exactly what I need", the Swiss said.