From what I see with some research,
this Reliable Sure-Lube is a grease cap. It's not the same thing as the
Reliable/Dexter Axle lube, which has a grease fitting on the end of the axle. With the
Reliable or Dexter you push grease in the fitting, It goes
through the axle to the rear bearing, through the front bearing and when the axle is full the old grease pushes out the front, around the edges of the axle where the filler fitting is.
The Reliable that does this has a rubber cap over the grease fitting, which is built into the axle and is not a metal dust cap.
I have a 95 Ranger Trail trailer with this type of setup, but mine isn't a grease fitting. The grease gun needs a needle type attachment instead of the regular grease gun fitting. It's a really good system.
What I see at the Trailer Parts Depot site is just a dust cap with a grease fitting; not the same thing. It's like a Bearing Buddy without the springs etc. So it seems like you'd be pushing the new grease in the front bearing, through the middle and finally to the rear bearing. There is no exit for the old grease.
If this is new to you, I agree with taking it apart to check the amount of grease and condition of the bearings and seal.
The alternative is to keep pumping until the grease comes out somewhere, probably around the seal.
Reliable Sure-Lube Grease Cap, 2K & 3.7K Axle Hubs, 1.98" Diameter, Sold As Each
www.trailerpartsdepot.com