If it is a published tool, cite only that tool and not anything that tool is. The publication of the tool will used should have citations for anything it used. In some cases you can adjust settings to programs inside that tool, you should make sure to mention any non-default settings.
However, some tools allow you to choose which sub-program you use. For example RSEM can use STAR, bowtie or bowtie2. You should cite this because it allows readers to see exactly what software you used to perform your analysis. RSEM can also take SAM/BAM files as direct input, so if you used something totally different, you should obviously cite it. In your case, if you selected MIRA over another program for MITObim, you should cite it. If MITObim can use MIRA and only MIRA, you probably shouldn't cite it.
If it is a custom script, cite the tools or libraries involved. As well as the author
A fuzzier case may be in instances where the item in question is more protocol than software (e.g. Trinotate). In that case you should probably cite the tools used.
There's always a judgement call in what level you stop at. The important thing is to generally cite things that contributed specifically to your analysis. I guess one way to think of it is what programs did you (or other authors) personally use directly, either by running the program or by specifying it specifically over another program. Giving credit is obviously important, but when dealing with methodological items (wet or dry) the most important thing is giving the reader enough information they could repeat the analysis.