HMAC(SHA-1) is an algorithm for Hash computation that also accepts a key as input value. The algorithm follows certain rules and guarantees a certain level of security and resilience against attacks.
Moving to its implementation: is HMAC(SHA-1) standard at the point that all the "official" and correct implementations of it produce exactly the same result for a given input message and key? Or is the algorithm accepting different implementations that might produce a different result?
any given implementation of HMAC-SHA1 will produce the same set of bytes given the same set of bytes as the input message and key.
That said, there can be a lot of variation on how various interfaces work and how they accept those bytes. For example, one library may output the hash as a hex string, and another may output it as an array of bytes. Or one would take a string as input with a UTF-8 encoding, whereas another would take it in as a UTF-16 encoding. You would need to be careful that the same bytes are hitting the algorithm in different libraries to ensure you get the same result.
Also, while HMAC-SHA1 is probably okay from a security perspective, you should probably be using HMAC-SHA256 instead.