Old-time means typical of what used to exist or used to be done. Old-time dancing, old-time values, an old-time shop. The feeling is usually warm, like a memory, not an insult. In American English, old-time music is also a set name for an older kind of folk playing, often with a fiddle. Elsewhere the phrase is looser: it just says “from those earlier days.” Like old-style, it almost always comes before a noun. You would not normally say “the music is old-time” the way you say “the music is old.” Friendly, everyday English.