The 29-year-old finally completed a switch to New York following a year-long pursuit by Millers boss Steve Evans and he made his full debut in Tuesday's Capital One Cup win over Sheffield Wednesday.
However, a thigh injury during pre-season training with Bournemouth meant his substitute's appearance in the season-opener at Crewe was his first action of the summer.
"Last week was my first bit of game time since five or six games from the end of last season, so I have had no game time whatsoever," Tubbs said.
"I have done a bit of running but had four weeks off with a thigh strain and after that I signed here so I've only had a week's worth of training.
"It might take a couple of games for me to get to my best."
Tubbs, who played under Evans at Crawley, initially joined the Millers on a six-month loan deal but has not ruled out extending his stay.
"I am never one to shut a door on anything, I will keep my options open which I think any professional should do," he added.
"So at the end of that six months who knows?"