Nobody seems to have mentioned to drill a long pilot through first so the cutter isn't been held back by the pilot bit then make sure you drill in from the outside brick to stop unsightly blast out, it dont matter too much inside as its covered by plaster.
The main advantage of dry cutting outside to inside with a diamond core is the majority of the dust and mess is deposited outside rather than inside the property and is easier to clean up. This is often only practical on the ground floor or if scaffolding is erected.
If you are getting 'blast-out' using a diamond core (cutting in either direction), your technique is wrong, you are applying to much forward feed pressure. The forward pressure should be minimal, just enough to keep the core centred and on track, the diamond lands will cut faster, more cleanly and with less heating of the core. Using the correct technique the exit should have no discernible break-out, or minimal break-out if the exit is through loose dry plaster.
Some of my left-handed colleges prefer to core drill with the drill in reverse (anti-clockwise) rotation, they say it's more comfortable, however this technique is not generally recommended as it risks unscrewing the core from the arbor.
Generally, a long pre-drilled pilot hole through the wall is not needed, but may be of advantage when cutting extremely hard materials eg. granite, or you are a novice core drill user and require the greater guidance. All that is required is to start the core with the pilot drill attached, once the core is centred and the diamond lands have cut to at least half the core's full depth, the pilot drill can then be removed, and rest can be cut with just the core, without it deviating significantly from your initial trajectory providing the forward feed pressure is not excessive.