I finally decided to look at the counting rates with a PMT HV of 1675 V. The attached figure shows a global plot summarizing all plots of the entry 333278, plus the counting rates at 1675 V (at the right on the chart, after the long HV switch off). We can remark that beyond a HV of 1600 V applied to the PMT, counting rate do not change by that much, meaning we probaly measure "what we have to measure".
Figure 1