Well, you switched from a monophasic pill to a triphasic pill, so it might take your body some time to adjust to having varying levels of hormones instead of having a consistent level as you did with the minestrin. Also, with ortho tri cyclen, I'm pretty sure the lowest level of hormone level it's that first week, then slightly higher the next week and then the highest level the third week before the placebos. So it looks like you had a breakthrough bleeding issue, which is totally annoying but not all that surprising.
Could just be because you switched types of birth control, and your body isn't used to it. I wouldn't say the Ortho caused your period to start.