These claims are compatible. For instance, lex, re2c, ragel, etc. are exponential in the length of the automaton description, but the resulting lexers work in linear time[1] in the length of the string. Here the situation is even better, because the DFA is constructed lazily, at most one state per input character, so to observe its full enormity relative to the size of the needle you need an equally enormous haystack. “One state per input character” somewhat understates things, because producing each state requires a non-constant[2] amount of work, and storing the new derivative’s syntax tree a non-constant amount of space; but with hash-consing and memoization it’s not bad. Either way, derivative-based matching with a lazy DFA takes something like O(needle + f(needle) × haystack) time where I’m guessing f(n) has to be O(n log n) at least (to bring large ORs into normal form by sorting) but in practice is closer to constant. Space consumption is less of an issue because if at any point your cache of derivatives (= DFA) gets too bloated you can flush it and restart from scratch.

[1] Kind of, unless you hit ambiguities that need to be resolved with the maximal munch rule; anyways that’s irrelevant to a single-RE matcher.

[2] In particular, introductions to Brzozowski’s approach usually omit—but his original paper does mention—that you need to do some degree of syntax-tree simplification for the derivatives to stay bounded in size (thus finite in number) and the matcher to stay linear in the haystack.