Should I worry about an initial negative voltage?
If you are using mBed then according to the Wikipedia article it probably uses an LPC1768 for which your favorite Internet search engine easily finds a datasheet.

Within the datasheet search for Absolute Maximum (sometimes Electrical specification). 

There is a Symbol called VI "input voltage". The description says:


  5V tolerant I/O pins; only valid when the VDD(3V3) supply voltage is present.


These pins are rated (absolute maximum) for -0.5V ... +5.5V, meaning that anything lower than -0.5V or higher than +5.5V may destroy your controller. It also means that if the voltage is well within this spec, you don't have to worry. 

To ensure your input will be within the given limits, you should consider using diodes to clamp the input to the power rails. Notice that your scope may not catch the highest peak!







simulate this circuit &ndash; Schematic created using CircuitLab

The Schottky diodes have a low voltage drop, well below the 0.5V room required.