First of all, let's rewrite your code a little bit, for the sake of removing some confusion (because to the uninitiated there are few things going on here, that might seem similar, but are not).
#include <string.h>
void print_as_according_to_strlen(char *n) {
    for (int i=0; i < strlen(newstring); i++) {
        printf("a");
    }
}
There, this is the relevant part. If you look at the definition of strlen you'll see, that it returns a value of type size_t
size_t strlen(const char *s);
Return the length of the string s.
size_t is an unsigned type. C and C++ have certain rules by which integer values are implicited converted to a "common" type when used together in an operation. These are the so called "integer promotion rules" – those are important to know, and you absolutely must learn them.
One of those rules is, that if you make a signed integer "interact" with an unsigned integer, the promoted type will be unsigned as well. And of course if you attempt to promote a negative value to an unsigned type, the result will be something different.
Now with C things become tricky here, because there are some (actually the majority of cases) where attempting to do that invokes undefined behavior, i.e. anything may happen. There are however a few exceptions, where it's actually well behaved (for example if you have two unsigned variables unsigned a = 3 and unsigned b = 5 the result of the operation a-b is actually a well defined value, because unsigned overflow is well defined, and the result is UINT_MAX - (b-a)).
The bottom line for you is: You must rewrite your code so that the comparison promotes to either a signed comparison, or instead of starting from -1, go to strlen(…)+1. Instead of using an int I suggest you use a ptrdiff_t instead, because the size of an int may, or may not, be sufficient to hold the result of strlen. And by happenstance (not of C, but how modern OSs manage memory) strlen will never return a value that could overflow ptrdiff_t
ptrdiff_t len = strlen(newstring);
for(ptrdiff_t i=-1; i < len ; i++){