I'm not sure if you're asking if the ball remained in possession past the goal line, or if the ball has to be inside the sidelines. I'll address both.
All scoring plays are reviewed by the booth official. If they had a concern with the review, they would have signaled to the on-field referee to wait if more time was necessary. Presumably they were comfortable with seeing that the ball broke the plane of the goal while still in possession. That's all done behind the scenes, so it's not possible to know how much concern or what was seen.
From my viewing, the ball remains in his outstretched hand until after he reaches the end zone and the ball appears to have crossed the goal line. It looks quite precarious in this image, but it looked that way for some steps before the end zone as well. I don't see anything to suggest that he lost possession before scoring.
You mentioned the ball was "outside the field". As long as the ball crosses the plane in possession, and the possessing player is in the end zone, then the ball can be beyond the sideline but still a valid touchdown.
From NFL Rule 11-2-1, subpart (a) was met:
ARTICLE 1. TOUCHDOWN PLAYS. A touchdown is scored when:
(a) the ball
is on, above, or behind the plane of the opponents’ goal line
(extended) and is in possession of a runner who has advanced from the
field of play into the end zone
It is only if the ball crosses the plane but if the runner does not reach the end zone that the position of the ball around the pylon is required.
This play is similar to approved ruling 3.16 (c):
A.R. 3.16 PYLON—GOAL LINE EXTENDED
Second-and-goal on B5. A2, running
to his right, is contacted by B2, and as he is going down at the B1,
he dives toward the pylon. The ball is held in his right hand extended
over the out of bounds area but beyond the extended goal line, when
his chest hits: ... (c) the
ground in the end zone. The ball crossed the sideline at the B½-yard
line, but it never went over the top of the pylon.
(c) Touchdown, as the ball broke the plane of the extended goal line, and the runner was not down until he was in
the end zone. (3-39, 11-2-1)