While researching this answer, I found that there's a bit of a discrepancy between Paris's pips prop and the dialog in "Caretaker", so there's two possible answers:
The "Caretaker" script is canon
The dialog in "Caretaker" indicates that Paris was, in fact, granted a field (provisional) commission and not a full commission:
JANEWAY: I've entered into the ship's log on this date that I'm granting a field commission of lieutenant to Thomas Eugene Paris. Congratulations.
If this dialog is to be considered canon, Paris's pips are just a production mistake.
Paris's pips are canon
If the pips are correct and Janeway's dialog in "Caretaker" is a writing mistake, in order to gain an official rank, an officer must have completed Starfleet training by graduating from Starfleet Academy, and his or her commission must be approved by Starfleet Command.
While he was briefly a member of the Maquis, Tom Paris was first a Starfleet officer who was subsequently dishonorably discharged and incarcerated prior to the events of "Caretaker". Captain Janeway reactivated him for the mission to hunt down the Maquis, and, since his reactivation happened prior to the mission, it was almost certainly approved by Starfleet Command and thus he was able to regain his commission.
Many of the other members of the Maquis we know of either never went to the Academy or dropped out before graduating (e.g. B'Elanna Torres), and thus could only receive field commissions once aboard Voyager. The members of the Maquis that were once Starfleet officers, like Chakotay, were also only eligible for field commissions as they could not be approved by Starfleet Command due to lack of contact.
An earlier example of the both provisions in play was Wesley Crusher in The Next Generation, who was granted a field commission of Ensign from Captain Picard. Picard couldn't give him a full commission because he never graduated from Starfleet Academy and Starfleet Command never approved it.
Which answer is correct?
In the background information for Tom Paris, Memory Alpha notes:
When Paris was promoted to lieutenant at the end of "Caretaker", he was given the rank pips of a full lieutenant and wore them for several episodes. However, as of the episode "Faces", this costume gaffe was corrected to reflect Paris' actual rank of lieutenant junior grade.
If true, given they noticed a mistake in the pip prop and purposefully corrected it with full pips, it would indicate to me that the latter scenario—that the dialog in "Caretaker" was a mistake and that Tom Paris did, in fact, receive a full commission prior to joining the crew of Voyager—is intended to be the correct one.