How are mitochondrial ATT (Ile) start codons translated as Methionine?
The key point in understanding non-AUG start sites in mRNAs is the nature and role of the initiator tRNA. 

There is a special initiator met-tRNA which differs in structure from all the elongator tRNAs in such a way that it — and only it — is recognized by the IF-2 type initiation factors (and not by the EF-Tu/EF-1 elongation factors). In a complex with the initiation factor and GTP it can bind to the ribosome at the P-site. Normally the ribosome will also be interacting with an AUG codon at the P-site, but in some cases it is not, so that initiation may still occur. 


  Thus, the initiating amino acid is always methionine, regardless of
  the codon, because methionine is the only amino acid with which the
  initiator tRNA can be charged.


In the case of bacterial mRNAs, it has long been known that about 10% start with other codons, predominantly GUG. This can be explained by their relative position to the ribosomal binding site on the mRNA — the Shine and Dalgarno sequence. I imagine this is what happens in mitochondria.

In the case of eukaryotic cytoplasmic mRNAs, an initiator met-tRNA complex normally scans from the 5ʹ-end, initiating at the first AUG or first the first AUG in an ‘appropriate context’. The precise definition of an appropriate context is unclear, and on can imagine that in some cases such a context pauses the ribosome at a non-AUG codon, at which initiation begins.

References

“The Biochemistry of the Nucleic Acids”, 11th edition, Chapter 12 (1992) RLP Adams et al. — this has all the older original references, but not the recent ones.

Wikipedia entry on Shine and Dalgarno sequence.

Eukaryotic scanning model: Hinnebush review (2011)

Initiation in prokaryotes and eukaryotes Londi review (2015)

Related SE Biology Answer on initiation and elongation met-tRNAs (by me)