Jules, here´s a bug report. This doesn´t happen for the Juce Demo 64 bits, only with the Juce Audio Plugin VST Demo 64 bits and MSVC2013. (I don´t have any other compiler to test, sorry)
This also happens with the ToolTipWindow, so its something related to fonts or font-sizes? For the test below all I did was compile the Juce Audio Plugin VST Demo, did nothing but added an AlertWindow to test.