With Australia having no official first-class warm-up matches ahead of next week's first Test against England at Edgbaston, this fixture represents a final chance for players to push their case for a place in an Ashes squad due to be named on Friday.
At Tuesday's close, the Graeme Hick XII were 96 for seven, still nine runs adrift of the Brad Haddin XII's 105 all out in 42.5 overs, with the two teams named after members of Australia head coach Justin Langer's staff in ex-England batsman Hick and former Australia wicketkeeper Haddin.
Seamers Michael Neser (four for 18) and Jackson Bird (three for 28) both impressed, while Australia A batsman Marnus Labuschagne made 41 for the Brad Haddin XII.
Fast bowler Cummins underlined his Ashes credentials with a haul of three for 15 that included bowling former Australia captain Steve Smith, who made nine for the Graeme Hick XII, off an inside edge.
Australia Test captain Tim Paine won the toss and put the Brad Haddin XII into bat on a well-grassed pitch that made life difficult for batsmen.
Openers David Warner and Marcus Harris both fell cheaply inside the first seven overs, before Labuschagne held firm for a time.
When the Graeme Hick XII batted, Ashes hopeful Cameron Bancroft was struck in the groin by a delivery from fast bowler Josh Hazlewood.
Mitchell Marsh hit a rapid 29, which included six boundaries, before he was bowled by experienced paceman Siddle, who took three for 20.