Since this question is really about new java.time-package and NOT SimpleDateFormat I will cite following relevant section:
Year: The count of letters determines the minimum field width below
  which padding is used. If the count of letters is two, then a reduced
  two digit form is used. For printing, this outputs the rightmost two
  digits. For parsing, this will parse using the base value of 2000,
  resulting in a year within the range 2000 to 2099 inclusive.
We see that Java-8 uses the range 2000-2099 per default, not like SimpleDateFormat the range -80 years until +20 years relative to today.
If you want to configure it then you have to use appendValueReduced(). This is designed in an inconvenient way, but possible, see here:
String s = "150790";
// old code with base range 2000-2099
DateTimeFormatter dtf1 = 
  new DateTimeFormatterBuilder().appendPattern("ddMMyy").toFormatter();
System.out.println(dtf1.parse(s)); // 2090-07-15
// improved code with base range 1935-2034
DateTimeFormatter dtf2 = 
  new DateTimeFormatterBuilder().appendPattern("ddMM")
  .appendValueReduced(
    ChronoField.YEAR, 2, 2, Year.now().getValue() - 80
  ).toFormatter();
System.out.println(dtf2.parse(s)); // 1990-07-15
By the way, if you really want week-based years then you have to use Y instead of y or the appropriate field IsoFields.WEEK_BASED_YEAR. Regarding the fact that you don't have any other week-related fields I would assume the normal calendar year, not the week-based one.