Monique,
I'm not sure about when to transplant the seedlings, but I do know that the spearmint will take over if you plant it in the ground, be sure to contain it. Lavender is very hardy any will come back every year even in Long Island.

Personnally these kits are useless. The containers are way too small for the mature plants.
Lavendar likes dry hot conditions. If you can keep yourself from overwatering in a container by all means pot in a container at least 6" across by at least the same depth. For optimal success plant outside in a location that gets the most sun and is relatively dry during the season. During the first couple months though you will have to water regularly until you notice it is thriving. In the pot after the seedling has started thriving allow the soil to dry out between watering.
Dill,is an annual. Depending on what kind you have it is best planted outside in the ground. If it is a compact variety you may get away with planting it in the same size container as the lavendar but don't let it dry out like you would the lavendar.
Rosemary is best grown under the same conditions as lavendar.
Spearmint by all means pot it in a container. You can use the same size pots as above but you will need to repot every year or so.
Congradulations on getting this far, make sure you don't under or over water. The best time to transplant is once you have 2 or 3 sets of true leaves (which are the leaves that appear "after" the first seedling leaves). You can use a regular soil-less potting soil like ProMix. All of these will be best grown outside, so when you transplant the seedlings into a larger pot keep the pots out of direct sunlight for a day or two, then over several days slowly increase the number of hours of direct sunlight they receive. This is called harding off your seedlings. Then place in full sun for the summer & fall. Once fall comes that is a different story.
Good luck
Karen

Thank you for your replies.

Karen- I am printing yours and following it to the "T"!

Monique