No, the bleeding you had is most likely due to slight hormonal changes due to doubling of the pill and not due to pregnancy or implantation bleeding.
Implantation bleeding - This is seen in 33 % women who are sexually active, and seen about 5-10 days after conception just around the timing of their periods. The bleeding is scant and colored pinkish or brown. This bleeding can sometimes confuse women who think that their period has come early, but only realize they are pregnant weeks later. Implantation bleeding will not be mid-cycle as in your case.
In addition, since you had sex in the last week of your previous cycle, during which you were also on birth control, there is no chance of ovulation, and hence no pregnancy is possible.
I hope this clears your doubts.