"I've got that side [on Monday] I want to be able to throw that, "Tillman said. "So, they pulled me off the field kind of quick."
The 21-year-old, who has dealt with back tightness in the past, attributed Sunday's discomfort to falling asleep on a couch on Saturday in an awkward position.
Tillman was not scheduled to throw on Sunday and after his back tightened up during several morning drills, he exited the practice fields at Ed Smith Stadium with one of the team's athletic trainers.
Both manager Dave Trembley and pitching coach Rick Kranitz -- who hadn't even heard of the minor injury -- were confident Tillman's throwing schedule for the rest of the week won't be altered.
"I don't expect [Tillman missing Monday's sideline] to happen," Trembley said.
Although the team hasn't announced any rotation plans, Tillman is widely believed to be the leading candidate to round out a staff that includes Kevin Millwood, Jeremy Guthrie, Brad Bergesen and Brian Matusz.
Bergesen has been working his way back from a strained right-shoulder capsule suffered while filming a commercial in early December, and continued to make strides with Sunday's flat ground session.
The 24-year-old, who said on Wednesday that he expects to be back on the mound within two weeks, is still on pace for that timetable. Following Sunday's 35 throws, Bergesen estimated he had 2-3 flat ground sessions left before getting back on the hill, possibly by the end of next week.
"Everything's feeling good," Bergesen said. "It's just that much better each and every time."
Trembley said on Sunday that Bergesen was "very, very close" to getting back on the mound, and the challenge now might be to slow the young pitcher down.
"He's anxious to get up on the mound, we're anxious to get him up on the mound. But there really isn't a rush to do that with him yet," Trembley said. "We feel like for as much progress as he's made, he's going to catch up [to the other starters] and be fine."
Bergesen was a pleasant surprise for the Orioles last year, going 7-5 with a 3.43 ERA in 19 starts, before a line drive to the shin on July 30 ended his season.
With the team's first full-squad workout slated for Tuesday, the Orioles home clubhouse is filling up fast. Nolan Reimold, Luke Scott and Garrett Atkins were among the newcomers to the team's Spring Training digs on Sunday, as more than a dozen position players worked out on the practice fields at the Ed Smith Stadium complex.
Trembley said Reimold is a full go in camp after undergoing offseason Achilles surgery on his left tendon. The outfielder had been running on the treadmill over the winter, but Sunday marked the first time Reimold had tested his Achilles outside.
"Obviously it's nice that he's here early," Trembley said of Reimold. "It's nice that [Felix] Pie's here, [Adam] Jones is here, and we will use common sense going through Spring Training drills with those guys."
The trio suffered season-ending injuries, but Trembley said the medical staff cleared Reimold, Pie and Jones in their pre-Spring Training report.
"They have no restrictions, they are all a full go," Trembley said. "We will monitor [them]; that's not to mean we will cut down on their workload."
Jones and Pie have both previously stated that they are back to full-throttle, and prior to Sunday's workout Reimold said he was confident he will be ready for Opening Day.
Reimold said he has no problems with the tendon now, but acknowledged it will be more of a test when he gets out on the field daily for several hours a day.
"After a lot of running, it still gets a little sore,'' he said, "But it's already better than it was last year. I'm sure I'll be ready [for Opening Day]."
Brittany Ghiroli is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.