The laws have changed through the years. There were a couple of factors involved in what your ancestors would have had to file. If they ARRIVED before 1906, they didn't have to provide proof of the date they arrived in the country and they only had to be residents of the country for five years and of the town they lived in for one year.
If they arrived from 1906 to 1924, they had to provide documentation of when they arrived, which ship, port, etc. They still had to be residents of the country for five years, but there were a couple of changes in that period about how long they had to live in the jurisdiction of whichever court they submitted their declaration of intent to before waiting one more year to take the oath of allegiance.
Between 1924 and 1951, the requirement changed and they would have to have resided in the US for a longer period. I'm not sure when the seven years came about, but I believe it was post WWII to give the government more time to research the background of refugees. I do have a chart with all the changes somewhere, but it's not in my filing cabinet, so I'll have to look around to see where I stuck it last.
But it really doesn't matter for these purposes. The 1906 Immigration Act changed the whole picture. Prior to 1906, they filed their declarations and petitions locally and that's where they stayed. But the 1906 reform standardized the forms...they were pre-printed and all the information was in a structured format that everyone would use...and not only was there a copy for the local court, but there was also a copy sent to the new Immigration and Naturalization Service.
Additionally, the records were indexed and filed by date. The only thing you need to know is the date of birth of the ancestor and you can get the records. The Chicago NARA center (National Archives and Records Administration) holds all INS documents from 1906 forward. The States may or may not have copies, but NARA has everything.
Here's a link to the NARA Center. BTW, if you do make the trip in person, also spend the rest of the day at the Newberry Library on the northside of the Loop (Gold Coast area). It has the best genealogy department in the Midwest, including records from all of the Great Lake States. It's a wonderful place to do research.