If we specifically talk about the case of twitter.com; As why site was not accessible from East coast and why it was accessible from rest of the world (roughly).
BGP routes announcement of same IP network from multiple locations and existence of infrastructure at various location is the answer of your query.
On doing the dig for twitter.com from multiple open-resolvers, i got multiple IP address for the said domain but they all belongs to same /24 IP network.
Kansals-MacBook:~ Kansal$ dig twitter.com A +short @18.104.22.168
Kansals-MacBook:~ Kansal$ dig twitter.com A +short @22.214.171.124
Kansals-MacBook:~ Kansal$ dig twitter.com A +short
Kansals-MacBook:~ Kansal$ dig twitter.com A +short @126.96.36.199
So, twitter site is hosted on 188.8.131.52/24 segment (getting an ip from this segment only from various locations; corner cases may exist).
On doing the WHOIS for this IP segment, i got to know that the following results -
Kansals-MacBook:~ Kansal$ whois 184.108.40.206
NetRange: 220.127.116.11 - 18.104.22.168
Parent: NET104 (NET-104-0-0-0-0)
NetType: Direct Assignment
Organization: Twitter Inc. (TWITT)
This means that 22.214.171.124/21 IP segment belongs to twitter.
Twitter has announce this segment (/21 or /22 or /24) from its various Data Centres (or from co-locations facilities) across the world.
So, when i request for twitter.com, i go to Singapore (as i am getting best routes from Singapore for this particular segment) And when someone tries to access twitter.com from East coast, he may have the best path for the segment from the location which was under DDoS attack.
Because of this announcement possibility of the IP segment from multiple locations and existence of infrastructure across the globe, service was only affected for few (locations which was under attack).
Hope this answers your query.