Here is a linguistic supplement to @naruto's answer:
This 「たって」 connects to the 連用形{れんようけい} (continuative form) of words. This is not immediately clear because of the euphonic changes that take place.
This is what happens when 「たって」 connects to 「言う」:
//iwu//の連用形+//tatte//
⇒ { inflect }
//iwi//+//tatte//
⇒ { //i// in //wi// devoices; consonant-consonant sequence //wt// repairs to //tt// }
//ittatte//
This is what happens when 「たって」 connects to 「言わない」:
//iwanai//の連用形+//tatte//
⇒ { inflect }
//iwanaku//+//tatte//
⇒ { combine; no devoicing or euphonic changes }
//iwanakutatte//
So it's essentially the same construction from the agglutinative perspective, just muddled a little by the euphonic changes which happen in the first case.
Bonus Content
You may ask: "Why is it //iwanakutatte// instead of //iwanakattatte//?"
Basically, this comes down to the syntactic status of 「たって」.
「た」 is a 助動詞{じょどうし} (auxiliary), while 「たって」 is a 接続助詞{せつぞくじょし} (conjunctive particle).
When you connect 助動詞 to 形容詞{けいようし} (i-adjective) (or a 助動詞 which inflects like a 形容詞), you need to insert a dummy verb //aru// which handles the 助動詞.
形容詞「高い」 connecting to the 助動詞「た」
//takai//の連用形+(//aru//の連用形+//ta//)
⇒ { inflect //aru// }
//takai//の連用形+(//ari//+//ta//)
⇒ { //i// in //ri// devoices; CC sequence //rt// repairs to //tt// }
//takai//の連用形+//atta//
⇒ { inflect //takai// }
//takaku//+//atta//
⇒ { //kua// compresses into //ka// }
//takakatta//
助動詞「ない」 connecting to the 助動詞「た」
//iwanai//の連用形+(//aru//の連用形+//ta//)
⇒ { inflect //aru// }
//iwanai//の連用形+(//ari//+//ta//)
⇒ { //i// in //ri// devoices; CC sequence //rt// repairs to //tt// }
//iwanai//の連用形+//atta//
⇒ { inflect //takai// }
//iwanaku//+//atta//
⇒ { //kua// compresses into //ka// }
//iwanakatta//
However, with a 接続助詞 like 「て」 or 「たって」, there is no need for the dummy verb //aru// with 形容詞:
形容詞「高い」 connecting to the 接続助詞「て」
//takai//の連用形+//te//
⇒ { inflect }
//takaku//+//te//
⇒ { combine }
//takakute//
形容詞「高い」 connecting to the 接続助詞「たって」
//takai//の連用形+//tatte//
⇒ { inflect }
//takaku//+//tatte//
⇒ { combine }
//takakutatte//
助動詞「ない」 connecting to the 接続助詞「たって」
//iwanai//の連用形+//tatte//
⇒ { inflect }
//iwanaku//+//tatte//
⇒ { combine }
//iwanakutatte//