You are confusing "prime" and "relatively prime."
Two positive integers $a$ and $b$ are "relatively prime" if and only if there is no prime that divides both. Equivalently, if the greatest common divisor of $a$ and $b$ is $1$.
A positive integer $p$ is a prime if and only if $p\neq 1$, and whenever $p$ divides a product $xy$, it follows that $p$ divides $x$ or $p$ divides $y$.
The totatives of $n$ are the integers $a$ such that $1\leq a\lt n$ and $\gcd(a,n)=1$; that is, that are relatively prime to $n$; not the primes that are smaller than $n$. If $p$ is a prime strictly smaller than $n$, then there are two possibilities: $p$ divides $n$, or else $p$ is a totative of $n$. So primes smaller than $n$ often account for several of the totatives of $n$, but they are not all the totatives.
So, the positive integers less than $36$ are:
- 1: $\gcd(1,36) = 1$, so $1$ is a totative of $36$.
- 2: $\gcd(2,36) = 2$, so $2$ is not a totative of $36$.
- 3: $\gcd(3,36) = 3$;
- 4: $\gcd(4,36) = 4$;
- 5: $\gcd(5,36) = 1$;
- 6: $\gcd(6,36) = 6$;
- 7: $\gcd(7,36) = 1$;
- 8: $\gcd(8,36) = 4$;
- 9: $\gcd(9,36) = 9$;
- 10: $\gcd(10,36) = 2$;
- 11: $\gcd(11,36) = 1$;
- 12: $\gcd(12,36) = 12$;
- 13: $\gcd(13,36) = 1$;
- 14: $\gcd(14,36) = 2$;
- 15: $\gcd(15,36) = 3$;
- 16: $\gcd(16,36) = 4$;
- 17: $\gcd(17,36) = 1$;
- 18: $\gcd(18,36) = 18$;
- 19: $\gcd(19,36) = 1$;
- 20: $\gcd(20,36) = 4$;
- 21: $\gcd(21,36) = 3$;
- 22: $\gcd(22,36) = 2$;
- 23: $\gcd(23,36) = 1$;
- 24: $\gcd(24,36) = 12$;
- 25: $\gcd(25,36) = 1$;
- 26: $\gcd(26,36) = 2$;
- 27: $\gcd(27,36) = 9$;
- 28: $\gcd(28,36) = 4$;
- 29: $\gcd(29,36) = 1$;
- 30: $\gcd(30,36) = 6$;
- 31: $\gcd(31,36) = 1$;
- 32: $\gcd(32,36) = 4$;
- 33: $\gcd(33,36) = 3$;
- 34: $\gcd(34,36) = 2$;
- 35: $\gcd(35,36) = 1$.
So the totatives of 36 are: 1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, and 35. Of these, 1, 25, and 35 are not prime numbers, but they are relatively prime to $36$. Of the primes smaller than $36 = 2^2\times 3^2$, neither $2$ nor $3$ are totatives of $36$.