The former world number one, whose previous outing was a surprise early exit at the hands of compatriot Magda Linette at the Miami Open last month, saw off home hope Siegemund 6-2, 6-3 in the last 16.
Swiatek parted ways with Wim Fissette following her second-round loss in Miami before linking up with Roig, who was part of Rafael Nadal's coaching team for many years.
The six-time Grand Slam champion has struggled for form so far this season, failing to reach a semi-final.
But Swiatek looked at home back on clay, the surface on which she has won 10 WTA titles including four French Open trophies, easily swatting aside Siegemund.
The Pole, who received a first-round bye as the third seed, broke serve five times in total as Siegemund never threatened an upset.
Swiatek will face either Alycia Parks or Mirra Andreeva in the quarter-finals.
Andreeva claimed a battling 5-7, 6-2, 6-4 win in the first round to eliminate reigning champion Jelena Ostapenko.
After winning the 500-level event in Linz last week, the world number nine has started her clay-court season in fine fettle.
Andreeva raced into a 2-0 lead in the round of 32 match in Germany, before Ostapenko clawed back level.
But the 18-year-old immediately regained the initiative by breaking in the fifth game to edge ahead once more.
The Russian creaked at the last though as back-to-back double faults when serving for the opening set at 5-4 and deuce let Ostapenko back in.
Ostapenko took full advantage of that reprieve by winning the next two games to claim the set, sealing the deal with a brutal cross-court backhand winner on Andreeva's serve.
Andreeva hit back by breaking the Latvian in the third game of the second frame.
Despite another untimely double fault at deuce when serving for the set, Andreeva held her nerve this time to hold and force a decider.
After exchanging breaks early in the third set, Andreeva pounced on Ostapenko's serve to get ahead 5-4 as she claimed victory in her first-ever meeting with the 2017 Roland Garros champion.
American Parks defeated Germany's Noma Noha Akugue in straight sets.
Earlier, fifth seed Jasmine Paolini collapsed to a first-round 6-2, 6-2 defeat against world number 79 Zeynep Sonmez.