No. It is very likely that you ovulated 12-36 hours after the first positive test.
The way ovulation tests work is that they identify the LH surge that brings on ovulation.
What you're supposed to do is to test daily, starting from a certain day in your cycle (depends on the average length of your cycle), at approximately the same time each day. When your test is positive (two lines of equal strength, or a test line darker than the control line), your ovulation is expected in 12-36 hours.
A test that you take after the first positive test is of no value - the LH may stay high or drop, but it's only the surge itself that's of interest.
Good luck!
Rachel