Step to reproduce the issue:
1. Open attached project.
2. Open scene named "DoubleFiringEvent".
3. Open the "Animation" window and in the "Hierarchy window" select game object "Animator".
4. In the "Animation" window select "Events" animation.
5. Enter the Play mode.
6. Press "Space" bar once to trigger the "Events" animation.
7. Notice that the "Console" window tells the time at which the event was fired and that it was fired only once. For instance:
Fired event at 1.00498
8. Clear the "Console" window.
9. Select the "Animator" game object in the "Hierarchy" window.
8. Find the "SlowFramerate" component in the "Inspector" window and drag the "Frame Rate" down to 5 (make sure that quality settings are set to "Don't Sync" ("Edit->Project Settings->Quality->V Sync Count")).
9. Again in the "Game" window press "Space" bar.
10. Notice that the "Console" window informs that there are multiple triggerings of the event. For instance:
Fired event at 1.752637
Fired event at 1.952537

Reproduced with:
5.4.0f3, 5.5.0a6.

Cannot reproduce with:
5.1.5f1, 5.2.5f1, 5.3.6p3.

Note1:
The issue is clearly explained in the video that was provided by the user.

Note2:
Changing Animator's "Culling Mode" to "Animate Physics" solves the issue.