In the very, very old days, the recording side was wound to the outside. It was dull because it was an oxide coating, and the acetate backing was shiny. Different transport designs required the opposite winding: the dull oxide side was wound facing the center, inside the pack. As tapes developed, manufacturers began to calender or polish the surface of the oxide in order to increase contact for better high frequency response and to reduce modulation noise. The backing became shiny PET film, and it was hard to distinguish the oxide from the backing. Premium mastering tapes are coated with a dull, carbon-based backcoating. This means that things have reversed for these tapes: the shiny side is now the oxide recording side.
Recordings are stored "tails" out for two reasons: 1) this leaves the reel in a played-to-end mode with reduced and uniform tension within the pack, and 2) print-through begins to affect tapes in a different flux pattern from that of reels stored with the beginning of the tape at the head. When the master tape is rewound to the beginning, print-through begins all over again; but the process now begins to erase the print signal created in storage. (Sometimes the audibility of a song before it is supposed to start is caused by groove deformation in a vinyl album. Large extrusions of the groove when the initial signal is very loud can affect the "no-signal" groove portion preceding the start of musical content. Good mastering can reduce that pre-signal, and it is rarely worse than print-through.)