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"If you’re Avoiding Notice at the start of an encounter, you usually roll a Stealth check instead of a Perception check both to determine your initiative and to see if the enemies notice you (based on their Perception DCs, as normal for Sneak, regardless of their initiative check results)."
it seems pretty clear from the text that the point of the Avoid Notice stealth check is to determine whether the enemies Notice you. if they don't, you begin the encounter Unnoticed.
the "based on their Perception DCs, as normal for Sneak" bit is merely telling you that the DC for the Avoid Notice stealth check is the same as the normal DC for Sneak (i.e., the enemies' perception DCs).
it doesn't mean that the Avoid Notice action works exactly like the Stealth action in every way, just that the DC's are the same.