A Cabinet Office press release about the alert, posted to its website at about 18:45 on Friday, was missed by many in the media, which meant there was little warning to the public.
Some campaigners have said this potentially jeopardised domestic abuse victims trying to hide secret phones they use to seek support and try to escape abusers.
Women’s Aid, the national charity aiming to end domestic abuse, is calling for more forewarning of alerts wherever possible.
Veronica Oakeshott, the charity’s head of external affairs, told News: “Survivors of domestic abuse frequently turn to second phones to help them access lifesaving support or flee from abuse.”
It is vital the devices stay hidden, she said, adding: “We would urge the government to forewarn the public that alerts might be issued, when possible.”
A government spokesperson previously said it was working closely with domestic abuse charities for tests of the system.
It has also been reported that senior government figures were discussing whether or not to send the alert hours before, on Friday morning.
Phil Garrigan, chair of the National Fire Chiefs Council, said on Monday he was grateful to the public for the response to the emergency alert.
He told Radio 4’s Today programme his organisation had seen a decrease in the number of wildfires emergency services have responded to in the last 72 hours.
Garrigan added that there were still four major incidents declared in Hampshire, Cambridgeshire, South Wales and the West Midlands.
Politicians, including Reform UK’s Laura Anne Jones and Andrew RT Davies for the Conservatives, have also questioned why the emergency alert was sent to phones in Welsh before it arrived in English.
The UK government did not comment directly, but said under the Welsh Language Act, it has to send alerts in the Welsh language first and sends alerts bilingually where possible.