UPDATE: According to Mumper, Blizzard is reviewing players that opened too many bags. While that's not a guarantee that your account will be expunged of any infraction (if you were wrongly banned for opening too many Tamer bags), it's good to know they are at least investigating the matter and re-looking at those who feel they did nothing to warrant it.
With the addition of the "bad luck protection" feature, Blizzard has taken a strong stance against gaming it. They now consider it an actionable offense if you open many bags all in one sitting.
Collectors from WarcraftPets are already reporting receiving temporary bans (3 days) for opening Tamer bags that they either saved from previous days or earned all in one day.
So just to be safe, better to open your bags as you receive them, rather than waiting until collecting all the Tamer bags for the day. It removes some of the fun for those that enjoying opening them all at once for that 'Christmas morning' feel, but until this is fixed it's better to be safe than sorry.
I use the term "fixed" lightly though, as it's unclear if this is actually a bug or if it's intended to stop players from trying to exploit the bad luck protection mechanic.