I don't use tuning apps, I use clip-on tuners of various makes and models.

For a dulcimer, you want/need one with a CHROMATIC setting. Some have settings for guitar, fiddle, ukulele, etc. and in that case you need to be sure that you are using the C setting. It's usually a very small letter and easy to miss until you understand its importance.

That same thing applies with an app. I' not aware that Fender ever made dulcimers, and I wouldn't be surprised if their all only had guitar settings

Here's some background info. The Fender app looks like it's made for specific instruments, guitar and uke and one more and only displays the notes that pertain to those instruments. Dulcimers need a tuner that displays all of the notes, a chromatic tuner. I use gStrings [android]. It is quite accurate and has advanced features you can use as you learn more.

MD standard tuning, Bass- D3, Middle-A3, melody- A3 or d4.

I\The dulcimer is a 1992 has never been played, the problem was the fender app. I downloaded a different app and used new strings all good. Checked the dulcimer again with the fender app does good on low D and A but not on melody strings. 

What is the length of the dulcimer's scale? And what size string were you tuning to D (I assume D5 (293.66hz)? Were the strings visibly old (rusty or black). Is this a used or new instrument?

Got my new Dulcimer today was built in 1992 supposedly has never been played. was tuning the first strings to D They vibrated sound low octave tried to tune them higher and the string broke was using an app from my phone. Not sure if the app was working correctly or just old strings.