Striker Teemu Pukki was away from the team on Thursday to be with his wife while they await the birth of their child.
"He missed the first week, so we have to be intentional how we integrate him in training," Loons interim coach Cameron Knowles said on video call from Tucson about Reynoso. "All those guys will go through the same process. We'll monitor their fitness, supplement their training as needed and then ramp them up so we have them all in a good place come start of the season."
Knowles called Fragapane's arrival "imminent," by Thursday night or Friday. Oluwaseyi and Hlongwane are expected shortly thereafter, Pukki some time after that.
"We need to give him as much support as we can," Knowles said. "He's a consummate professional and we know he's going to keep fit and train and be ready when he does return."
The Loons signed 20-year-old former Real Salt Lake midfielder Moses Nyeman, who was waived after last season, and 23-year-old Swedish center back Victor Eriksson. On Wednesday, they signed USL Championship defensive midfielder Carlos Harvey, 23.
New sporting director Khaled El-Ahmad has arrived in Minnesota this week and will join the team in Tucson on Friday afternoon for the first time, Knowles said.
The Loons played a preseason scrimmage against Sporting Arizona and will play another against MLS side CF Montreal on Saturday night.