Strictly as written, probably not, but it’s commonly allowed
Most seem to consider this more of a rules gap or accidental omission than an intended and appropriate limitation on the feat.
There’s no general rule for the ×4 multiplier that would apply
The primary source on skill points at first level is a couple of paragraphs and a table on page 62 of the Player’s Handbook that say
Determine the number of skill points your character gets. This number depends on his or her class and Intelligence modifier, as shown on Table 4–1: Skill Points per Level. For example, Lidda is a 1st-level halfling rogue with an Intelligence score of 14 (+2 Int modifier). At the start of play, she has 40 skill points to spend (8 + 2 = 10, 10 × 4 = 40).
A character gets at least 4 skill points (1 × 4 = 4) at 1st level, even if he or she has an Intelligence penalty.
A human gets 4 extra skill points as a 1st-level character. A human character with the same class and Intelligence modifier as Lidda would have 44 skill points at the start of play.
Table 4–1: Skill Points per Level
| Class |
1st-level Skill Points¹ |
Higher-level Skill Points² |
| Barbarian |
(4 + Int modifier) × 4 |
4 + Int modifier |
| Bard |
(6 + Int modifier) × 4 |
6 + Int modifier |
| Cleric |
(2 + Int modifier) × 4 |
2 + Int modifier |
| Druid |
(4 + Int modifier) × 4 |
4 + Int modifier |
| Fighter |
(2 + Int modifier) × 4 |
2 + Int modifier |
| Monk |
(4 + Int modifier) × 4 |
4 + Int modifier |
| Paladin |
(2 + Int modifier) × 4 |
2 + Int modifier |
| Ranger |
(6 + Int modifier) × 4 |
6 + Int modifier |
| Rogue |
(8 + Int modifier) × 4 |
8 + Int modifier |
| Sorcerer |
(2 + Int modifier) × 4 |
2 + Int modifier |
| Wizard |
(2 + Int modifier) × 4 |
2 + Int modifier |
1 Humans add +4 to this total at 1st level.
2 Humans add +1 each level.
(Player’s Handbook, pg. 62)
Note that the text doesn’t say anything about multiplying your 1st-level skill points—it just says to read the table, where the 1st-level skill points are all multiplied by ×4. Nothing says that’s a universal rule, it’s just a thing that all these classes—and (almost) all other classes—do. Perhaps more notably, humans aren’t said to add +1 to skill points per level (which gets multiplied ×4 at 1st), they’re said to add +4 at 1st and +1 thereafter.
Even the minimum skill points at 1st is simply defined as 4—the parenthetical explains where the number 4 came from, as 4× the usual minimum of 1, but the rule is still just “4” and the multiplication is an explanation, not the rule itself. (Contrast a situation where the rule was multiplication, and then it had a parenthetical “(4)” indicating what that value would be.)
Since Nymph’s Kiss does not say anything about getting a ×4 multiplier at 1st, as class skill points, human bonus skill points, and minimum skill points do, it probably does not, strictly speaking, get that, and you end up with (X + Int)×4 + 1 skill points at 1st.
Common practice favors consistency
In most cases, the bonus skill points from Nymph’s Kiss are multiplied by ×4, because this is consistent with the rest of the game. The precedents here are, in reality, pretty thin—just human and a few similar races with copies of humans’ racial skill point bonus—but it’s easier to just treat skill points per level as being multiplied ×4 across the board at 1st level.
(This would not apply, at most tables in my experience, to the feat Open Minded, which gives a static +5 skill points at the level you take it rather than increasing your skill points per level. That would remain +5, and not become +20, even if taken at 1st.)
If one doesn’t do that… then one has to consider the swordsage from Tome of Battle, which says
Class Skills (6 + Int modifier per level, ×6 at 1st level):
(Tome of Battle, pg. 16, emphasis mine)
If ×4 isn’t a global rule, and we’re supposed to just listen to what the individual element (human, class, Nymph’s Kiss) does or doesn’t say… the swordsage gets an unprecedented ×6 multiplier at 1st. Obviously, a DM is free to rule that all classes get a consistent ×4 multiplier, but a feat like Nymph’s Kiss does not, but that does feel a little inconsistent to me.
Another consideration here is the simple fact that with the ×4 multiplier, Nymph’s Kiss is an okay feat. Without it, it’s… pretty poor. Which is par for the course with exalted feats—only a handful or so are anything but awful. Nymph’s Kiss could be one of the exceptional ones, if you let it.
