Before anyone starts posting misinformation here like on the Stormwind version, let me clear things up:
You don't have to complete the BFA introduction for your faction before you can head back to Chromie and choose an alternative timeline to level in. What you do have to do is either:
Pick the dialogue option, skip the spoon-fed city introduction and just walk on over there and say hi.
or
Take the quest, finish the spoon-fed city introduction and then continue on with the first couple of quests into BFA content.
Once you leave starter island, you are offered up the quest welcoming you to your faction capital, Welcome to Orgrimmar. You are then given a small tour of the city, with a few extra quests showing you some game mechanics, before sending you off to meet the faction leader, ending the quest chain with An Urgent Meeting
At this point, you should be able to head over and talk to Chromie, coz the start island quests are officially over. However, Brekka will want to offer up Mission Statement the new version of the old Mission Statement which is may have be unavailable for your Exile Reach character, but is prolly still be available for old chars, and those made in the racial starter zones.
If you picked up this quest, or Chromie still is not available if you didn't and went to check, all you need to do is talk to Nath Blightcaller and either watch, or skip the cut-scene to arrive in Zandalar. There is no mission to free the Z trolls in Stormwind from this version of the quest, dunno if the old version is still active. Although you are expected to walk with Princess Z Troll to the see her dad, you an opt not to and simple port back to Orgrimmar, since you already set your hearth there as part of the noob questline. Princess Z Troll will wait patiently until you decide to return, and you will be able to take up Chromie's alternate questlines.
Basically, Blizzard wants to funnel you into BFA content, but you really don't have to. bare in mind, there' nothing wrong with BFA's leveling zones, it's the end game content that was bad.