When the long flexor tendon has tension it will increase ground reaction force at the tip of the toe.
Upward force on the tip of the toe will then to dorsiflex the proximal phalanx.
At the MPJ, the dorsiflexion moment from ground reaction force at the tip of the toe is greater than the direct plantar flexion moment from the long flexor at the MPJ.
(Which is what Craig said.)
So, with long flexor contraction you will get plantar flexion of the pipj, dipj and extension of the MPJ.
You can get even more complex if you bring in the action of other muscles.
For, example the sort flexors could contract simultaneously with the long flexor, you are much more likely to get a claw toe occurrence than if you contract the long flexor alone.
The long flexor by itself can cause plantar flexion of the pipj and then hyperextension of the dipj.
Try flexing your toes into the ground and sometimes you can get hammertoe or mallet toe or claw toe.
Contraction of the EHL will crate passive tension in FHL and this will also create a claw toe deformity (Extension of mpj and plantar flexion of dipj and pipj.
Eric