People kept arriving at the centres, particularly from low-lying areas and communities near overflowing rivers.
"It's raining and getting cold, especially for the elderly and children. A lot of them said that all their stuff was taken by the floods so they came up with what they were wearing at the time."
The Red Cross was giving out emergency supplies, collecting rainwater, repairing sanitation and distributing lanterns to people who remained without power.
Foreign Minister Murray McCully said Samoan authorities were coping "extremely well" with the situation and had not called on New Zealand for assistance, but help would be available at short notice if required.
Cyclone Evan could develop into a category five monster by the time it hits Fiji.
Fiji Meteorological Service director Alipate Waqaicelua said the cyclone was still hovering over Samoa last night, with sustained winds of up to 170km/h, and brief gusts almost double that.
He said it would likely turn into a category four by this morning.
"It is expected to reach Fiji by Sunday afternoon as a category four and possibly a category five. At this stage there is nothing in its way to destroy its structure so it's got everything favourable for it to develop further."
Mr Waqaicelua said Tonga and Wallis and Futuna would likely be hit with gale-force winds but would probably be spared the full force of the cyclone.
Fiji's Prime Minister Commodore Frank Bainimarama issued a statement urging every Fijian citizen to take the "impending disaster" seriously. "I call on you to secure your homes, your businesses and your properties. I also urge you to now stock up on emergency and essential items. Every Fijian must be prepared and not be complacent."
"Fellow Fijians, I cannot stress enough how serious this is."
Maungakiekie MP Peseta Sam Lotu-Iiga says it is sad to learn of the deaths of three people in Samoa, two of them children and that his prayers and sympathies go out to the families and villages affected.
Family members of New Zealand Idol winner Rosita Vai also lost their home in Cyclone Evan.
The 31-year-old was due to sing at Samoa's Christmas in the Park today with Kiwi rapper Scribe, but the event was cancelled after the wild weather.
Ms Vai and Scribe are staying at the Tanoa Tusitala Hotel in Apia, with other tourists seeking shelter.
Ms Vai, who won the second season of New Zealand Idol in 2005, said on Facebook: "We have stocked up ready for the inevitable ... we are safe at the moment. To all the beautiful darlings here in Samoa, be safe, alofa atu (much love)."
She added: "Thankful my famz are safe even though they lost their house in the cyclone - the floods may have taken their personal belongings but praise God they are alive. Some are now here staying at Tanoa (Hotel) with us ... To all who are affected by Cyclone Evan, nafo sauniuni (be prepared).
"Miss my family, my man back in NZ. I love you Samoa. Jesus take the wheel."
Ms Vai was to perform at Apia Park tonight with Scribe and New Zealand-based singers Melenau Lino and Bella Kalolo, London-based soprano Aivale Cole and Australian Idol finalist Angel Tupa'i. Scribe - real name Malo Luafutu - was also in the country for his wedding.
He had been in the presidential suite of the Sinalei Reef Resort & Spa when the windows were blown out. "The windows just smashed in like an explosion and cut me and my new wife, and then [we] barricaded [ourselves] inside the bathroom," he said. "I got some mattresses inside the bathroom. It actually seemed like a bomb the way it exploded."
Journalist Jonah Tui Le Tufuga told Radio New Zealand the damage in and around Apia was worse than both cyclone Ofa in 1990, which killed seven people, and cyclone Val in 1991, which killed 16. "It is phenomenal. I have experienced both Ofa and Val and I believe they have nothing compared to what Evan has done within 24 hours," he said.
"A lot of families are coming back to skeletons of their homes and most of their belongings being swept away when the river banks burst yesterday afternoon."
NZ MetService duty forecaster Philippa Murdoch said at this stage the cyclone would not have any significant effect on New Zealand's weather.
The numbers
3 - Killed by Cyclone Evan
3000 - People forced from their homes in Samoa
200 - Injured by flying debris
