Android: Alarm starts at wrong time

Question

On some devices (even on some that, at least according to the manual, do not have a battery saver in the system, and the customers deny they installed one) the system broadcasts the Alarm Intent several hours later, only at the moment when the user switches the device on.

If the users set the alarm in a few minutes, it works. If it is set in a few hours, it might work, might be off by a few minutes or hours, most likely the latter.

This is getting on my nerves, as

1. I always get the complaints from the customers (understandably), and

2. I do not have a generic answer for them, as it might not be obvious where the problem lies, where to exclude my app from that "unexact" behaviour.

3. it is not even an 'about' time when it's several hours wrong!

I do target API >= 19/KitKat, so I distinguish already how to set the alarm:

            PendingIntent pi = PendingIntent.getBroadcast(ctx, 1, i, PendingIntent.FLAG_UPDATE_CURRENT);

            if (android.os.Build.VERSION.SDK_INT >= 19)
                alarmManager.setExact(AlarmManager.RTC_WAKEUP, calSeqStart.getTimeInMillis(), pi);
              else
                alarmManager.set(AlarmManager.RTC_WAKEUP, calSeqStart.getTimeInMillis(), pi);

Often, and also in the latest case it's not even an API 19 device:

TCT ONE TOUCH TAB 7HD (TAB7HD) OS API Level: 16

To the code: I am sure "calSeqStart"'s time is correct, this cannot be a problem.

It cannot be a WakeLock problem, as soon as the BroadcastReceiver gets the Intent, it logs a message, and that message also appears at the wrong time! So the broadcast is sent only at the time the user switches the device on.

At my place, and hundreds of others, it works without problems.

My questions:

1. How can an Alarm App tell the system forcibly it needs to be woken up and started at a certain time?!
2. Does anybody know whether it's possible to find an energy-saver-app like STAMINA (Sony Experia Z) so that the user can be warned?

ADDITION:

In my app, I do set alarms in the alarm manager as AlarmManager.RTC_WAKEUP type, but when I dump the alarms using adb, I see they are mapped to AlarmManager.RTC type.

This only happens on some (or at least one: Alcatel onetouch TAB 7D) device. On all others, the alarms set by my app do correctly wake up the device (and I see them as RTC_WAKEUP in the "adb shell dumpsys alarm" as expected).

As it is Android 4.1.1, it cannot be an AppOpps check, must be something else.

And using the ADB, I see that only deskclock can set the alarm as WAKEUP, all entries of other apps are non-WAKEUP alarms.