It will advance based on its class
In brief, you only can get the feat at first level, so you need levels, and that means you need a class. Because a specific clause forbids you to take the feat when you have multiple RHD, you only can take it if you have a single HD, and such monsters improve based on their classes HD, not on their former monster racial HD.
Monsters with multiple RHD
Let's use an example: you start as a centaur. This is a creature of type Monstrous Humanoid, race Centaur with these Racial Hit Dice (RHD):
Racial Hit Dice: A centaur begins with four levels of monstrous humanoid, which provide 4d8 Hit Dice
RHD work like this
Racial Hit Dice A number of the minor races, particularly nonhumanoids, begin play with some number of Hit Dice derived from their monstrous race in addition to any Hit Dice for their class levels. For example, a centaur has 4 Hit Dice as his racial base before he adds any class levels.
You first apply the racial Hit Dice, before you add any class levels. While they impact various other properties, they are not class levels. Now you modify it. The Improvin Monsters rules tell you
there are several methods by which extraordinary or unique monsters can be created using a typical creature as the foundation: by adding character classes, increasing a monster’s Hit Dice, or by adding a template to a monster. These methods are not mutually exclusive—it’s possible for a monster with a template to be improved by both increasing its Hit Dice and adding character class levels.
Human Heritage has this restriction :
This feat may only be taken at 1st level.
That means to get it you need to add class levels, because while they increase your effective level, neither RHD nor tempate modifications are levels per se, and you need to be 1st level to take the feat. So far, so good. Unfortunately, Monsters as Races tells us
Characters with more than 1 Hit Die because of their race do not get a feat for their first class level as members of the common races do
So, as you do have more than 1 RHD, you do not get a feat for your first class level, and thus cannot take the feat which you only can take at first level. The question what kind of Hit Die you would advance thus never arises.
Monsters with a single Hit Die
Alternatively, let's assume you are a Pixie, a Fey who has a single d6 Hit Die. It specifically tells us
A pixie character exchanges its 1 HD of fey for its first class level.
(I picked a non-humanoid monster type on purpose here, but it works the same for humanoids, see the Type rules:
Humanoids with 1 Hit Die exchange the features of their humanoid Hit Die for the class features of a PC or NPC class. Humanoids of this sort are presented as 1st-level warriors
This also matches the general rules for Monsters as Races
If a monster has 1 Hit Die or less, or if it is a template creature, it must start the game with one or more class levels, like a regular character.
Creatures with 1 or less HD replace their monster levels with their character levels. The monster loses the attack bonus, saving throw bonuses, skills, and feats granted by its 1 monster HD and gains the attack bonus, save bonuses, skills, feats, and other class abilities of a 1st-level character of the appropriate class.
So in this case, you do not have racial HD, you only have a single class HD. Let's say you pick Fighter, to be able to take the feat. The feat then has this effect:
You are treated as a humanoid with the human subtype for the purpose of adjudicating all effects. If you are not a humanoid, your type changes to humanoid and you gain the human subtype. If you are already a humanoid, you gain the human subtype. In either case, you retain any other subtypes you had (such as orc or extraplanar), and you retain any traits common to all creatures of your original type (such as darkvision).
So your pixie now is a Fey Fighter Level 1, that is also considered to be a Human. Hit Dice type is a Feature, not a Trait, so they are not one of the traits kept (and anyways have been replaced by the class HD).
Can you now add more RHD? The Improving Monsters rules say:
Intelligent creatures that are not humanoid in shape, and nonintelligent monsters, can advance by increasing their Hit Dice
(That is why we picked a non-humanoid; humanoids cannot do that). What hit dice do they now finally increase?
Note that if a creature acquires a character class, it improves according to its class, not its type.
And, under Advanced Monster Challenge Rating
When adding class levels to a creature with 1 or less HD, you advance the creature like a character. Otherwise, use the following guidelines.
This is pretty consistent: you do not add more racial HD to a 1-HD monster that has a class. You advance it as a character, based on the class. Only otherwise, you would use the guidelines that follow and that talk about RHD. This is not otherwise, so you add more of the HD that the monsters class has.
