LH testing is not entirely foolproof and there are conditions in which the LH level can rise before ovulation and give a false positive urine test result (polycystic ovaries is one). One thing a fertility clinic might like to do is perform another ultrasound scan 24 hours after insemination to make sure that the follicle has indeed ovulated.
Some clinics perform two inseminations 24 hours apart, to make sure to hit the ovulation window. Even in the most careful and successful clinics, DI does not produce pregnancy rates much above 10 per cent per cycle, so correct timing does not solve all the problems, nor does it seem to be absolutely critical.