That's correct you would need to raise the front of the scope. However that's almost never necessary. I'd check your mounts and rings carefully to see that something isn't amiss. Typically the problem is the scope needs to look down rather then up requiring elevation of the back part of the scope. There also is the possibility that you have a internal scope problem.
My guess off the top of my head is your rear mount is sitting too high and it could be from adjusting the scope recoil pin too deep into the hole provided( to keep the scope from walking ) to allow the mount to clamp into the dovetail correctly.
I'm making a lot of assumptions here. Are you dealing with a springer air gun to start with? I've never had to elevate the front of the scope in all my years of shooting.
With a scope simplest way it's to think what happens when you move the cross hair relative to the target. If you lower the cross hair you have to raise the gun (barrel) to re-aquire the target. This fellow said he's shooting high so he if he raises the cross hair (in the scope) he would have to lower the gun to re-acquire the target lowering the barrel relative to the target resulting in lower POI . He's reporting that he's out of adjustment so his option is to raise the scope. Assuming the reticle is positioned forward of the middle of the scope he'd want to raise the front of the scope. I've had the opposite plenty of times at long range running out of vertical adjustment. Moving scope adjustment so the cross hairs were lower causing me to elevate the gun. When you run out of adjustments in this case you have to tip the scope up in the back and down in the front. I've never had to do the opposite.
To be off that much, and in that direction, I believe something is amiss in your mounting. Try reversing your rings, front to rear. if the problem reverses, then you may have a ring that is out of spec. If you have had other rings on the same rifle without issue, then that is almost for sure the problem. If the situation is the same with rings reversed, or, with other rings, then you have a barrel alignment issue, and you will need to either shim the front ring as described, or, try adjustable rings, there are numerous ones available. Scope damage using shims is not a problem if you use reasonable torque on the screws, and the amount shimmed is not extreme. I often use a .020" (roughly 20 MOA) shim and have never had a problem. My experience is with PCP rifles. If this is a spring piston rifle, then you could have some scope movement at light screw tension, and you should use either adjustable rings, or, a drop compensating mount (used in reverse in your case).
A couple decades ago I tried a couple different adjustable scopes finding that after a couple hour "setup session" mounting the scope, shooting a group to test the poi, unmounting the scope, readjusting the mount, remounting the scope, shooting a group to check the new poi (so on and so forth). My experience was simply that the adjustments "shot loose" during the seasons I shot about 1200 pellets a month from my rather stiffly tuned .177 R9 (7.9 grain CPL @ 910-920fps).
Out of frustration caused by the tedious "adjustable scope mount setup", only to have the adjustment shift with use I started simply bending my barrel and I've been "barrel bending" ever since. Personally, I don't do any "scope tube shimming" either due to the possibility of damaging the scope. I simply "optically center" the reticle, mount the scope to my R9 or HW95, then bend my barrel till the poi at my zero distance (25-30yards depending) is about 1" from the aim point, then I do the fine adjustments with the scope turrets.
Anywhoo.........a barrel can be bent enough to move the poi 4" at only 18 yards and the bend can't be seen with the naked eye! I learned this when I made the mistake of using a RWS Lock Down Mount designed for the RWS normal "barrels with droop" on my .177 Beeman R9 which didn't have droop. LOL.....I simply trashed the RWS Lock Down mount with it's ".025" ElevationCompensation for Barrel Droop" reverting back to to a "non-ElevationCompensation for Barrel Droop" mount and re-bent my barrel as necessary.