When the new event begins, you must login to start getting sigils. If you wait until Friday, you will miss those for Mon thru Thu. If you login Mon but don’t have time to fight until Fri, you will still get those 16 sigils.
This might be the case, but it has been stated repeatedly that you are supposed to accrue sigils on days even if you aren’t logged in. Looking back at prior report of this issue… there is also the “didn’t play on the day the event started” as a common factor to having missed sigils mentioned. It is likely that sigils are accrued for any live event whether you log in or not, but only starting the first day you logged in after the event started.
See this unresolved bug report (initially reported a year ago, last replied to two months ago):
Suggest following up with a support ticket, since it is clearly documented how it is supposed to work.