I'm using QGIS 2.14.3 - Essen (but have also tried 2.18.12 Las Palmas)
Using 2.14.3, if I select one feature in a vector layer, and then use [Vector][Research][Select by Location], I have the option to check the 'Only selected features' option (this feature is not available in 2.18.12). The analysis behaves as one would expect if only the selected feature is used.
In newer releases, the dialogue box doesn't have an option to only analyse selected features and the outcome is different to case 1 above (in that all features in the layer are processed, irrespective of how many may be selected)
I can see that in [Processing][Options][General], there is an option to 'only use selected features' but it appears to me that this is not used - irrespective of whether this box is checked or unchecked, the select by location algorithm uses all features, not selected features.
Processing > Options > General
and make sure the Use only selected features option is checked. Now when you run your processing algorithms, it should only run on those features which were selected. On a side-note, you should consider downloading a more recent version of QGIS (currently 2.18).Save As...
option to save the selected features as a new shapefile and then run theSelect by location
tool on this new shapefile :)