I find it difficult to answer ihines question without knowing what year triumph he is talking about.
Fair enough but it should be simple to figure out:
If it is a 1963-1969, that breathes through the end of the camshaft, it uses a seal and the spring faces the sprocket.
If it is a 1970 or later, that breathes through the primary (no matter what the 1970 parts book says), it does not use a seal.
While you may have found seals in non-seal cases, or seals with the spring facing inward, it is not how it was designed to work. It was not how they were installed by the factory.
Is there any harm in installing a seal backwards in a 1963 to 1969? Other than cases where one chooses to use automatic transmission fluid in the primary, probably not.
May I quote the Overhaul manual
written by Tom Gunn and used exclusively in the Triumph "Tri-Cor" Dealer Service School:
"o) Install the primary crankshaft oil seal open side (wire ring side) facing out toward the primary.
(note: authors underline) DO NOT drive the seal all the way in - it must not seat against the drive side bearing and cause a drag on the crankshaft."
Is there any harm in installing a seal in a 1970 or later, that breathes through the primary, Yes! Basically the engine will not breath and the crankcase pressure will rise. This increases the chances of oil leaks and premature gasket failure.