Those apps definitely aren't accurate. I personally recommend not using them and using a paper chart instead. I also recommend doing full on symptothermal cycle charting. It can help you predict your late periods ahead of time and it can ease a lot of the late period anxiety.

It works based on the fact that after your ovulate, your core body temperature goes up just a tiny bit because of the progesterone in the luteal phase of your cycle. You use a special highly sensitive thermometer (they're pretty inexpensive) and take your temperature at the same time upon waking every morning. You chart this out on a graph, and then look for patterns. In a cycle with normal ovulation, you have what is called a bi-phasic pattern. You'll see a bunch of low temperatures during your follicular phase, then a tempterature spike around ovulation and then the tempteratures should stay up until your next period (this is your luteal phase). For most women, their period comes about 2 weeks after the temperature spike. Mine ususlaly comes 11-12 days after. Everyon'e luteal phase length is a little different, but your own phase length is pretty much set down to a day or two. Once you know how long your luteal phase is, you'll be able to predict when your periods will come a lot more accurately than an app can.

You can identify anovulation by the lack of a discernable temperature spike on your chart. When you're not ovulating, it's also possible to not have a real period. If you go long enough without ovulating, the uterine lining just gets too heavy to stay in, and you can get bleeding at strange times. It's not a true period because you never actually ovulated.

All of the above is a pretty rough simplification. Don't try this without reading a proper guide on how to interpret charts. I recommend the book, Taking Charge of Your Fertility. It will also help you identify abnormalities with your cycle or cervical fluid and know when it's time to see a doctor if something is off.