No rule specifies the order that natural attacks must be made in.
As per this question, when a creature has iterative attacks due to a high base attack bonus, they most take those attacks in order - attacks made at the highest BAB happen first. You might think the same rule should apply to natural attacks, and so primary attacks must go first (as secondary attacks have a -5 penalty). However, the precise wording of the rule from the description of the Full Attack action is:
If you get multiple attacks because your base attack bonus is high enough, you must make the attacks in order from highest bonus to lowest.
More generally, the intention seems to be that when you are granted iterative attacks (multiple attacks with a single weapon) of any kind you must make those attacks in order of descending BAB, so this applies even if you are gaining extra attacks because of Haste, or a being a monk making a flurry of blows, or whatever.
Multiple attacks gained from multiple natural weapons are not iterative attacks, though. You only ever get a single attack per action with any of your natural weapons, and multiple attacks are gained by simply having multiple weapons, not iterative attacks due to BAB or other sources. The rule is simply that primary attacks are made at full BAB and secondary attacks are made at -5 (or -2, if the creature has the Multiattack feat). There's nothing stopping you making natural attacks in whichever order you so choose.
In this post by James Jacobs, Pathfinder's creative director, referring to the replacing 3e's separate "Attack"/"Full Attack" stat block sections with a single "Attack" entry, he states:
And now that in Pathfinder a monster's primary and secondary attacks are determined by the type of attack and not when in an attack sequence they occur, there's even LESS of a reason to maintain the split.
Which would indicate that primary attacks and secondary attacks do not have to occur in any kind of order, and certainly that a primary attack which is made for whatever reason after a secondary attack does not get downgraded to a secondary attack.