To elaborate a bit on the comments:
The Tokenizer (AKA Lexer) will always process you input stream producing a stream of tokens for the parser rules to use when recognizing your source structure.
The only "order of invocation" is that the Tokenizer runs before the parser (an obvious necessity, since the parser acts on the tokens produced by the parser).
For lexer rules, all rules are logically applied against your input stream. If you have more than one Lexer rule that can match the next characters in your input then, two rules come into play.
1 - If one Lexer rule matches a longer set of characters then it will be used to produce the token.
2 - If more than one rule matches the same number of characters in your input stream, then the first of those rules to appear in your grammar will "win"
fragment
s are not lexer rules. They are just a convenience you can take advantage of to compose Lexer rules to avoid repetition and aid readability.
In the parser, you choose the starting rule, and then the parser processes the contents of that rule (recursively calling the rules that make up that rule and it's children, etc.). The only "order" involved there is that ANTLR will evaluate top level alternatives in a rule in order and this can be used to address things like proper operator precedence in arithmetic expressions, etc.