Demonstrations followed the Supreme Court's decision on Wednesday to free Asia Bibi with hard-line Islamists blocking roads in major cities.
The mother of five had been on death row for 8 years but always denied any wrongdoing.
April, a South Asia specialist at Christian Solidarity Worldwide told Premier she was concerned for Christians and the charity's partners on ground.
Speaking during the News Hour April said: "What we understand from our partners is that the situation is actually getting worse.
"The government have actually imposed blocks on social media, on telephone services, on communications - there's also a media blackout."
Demonstrators in Pakistan have vowed to keep rioting until a decision to free Bibi from death row is reviewed.
Pakistan's prime minister Imran Khan has called for calm and said hard-line Islamists were "inciting" people for their "own political gain".
April told Premier the blasphemy laws were still of great concern.
She added: "What's going to happen the next time a Christian's accused of blasphemy?
"We'll be in the same situation so I think the government need to try to contain the situation, get a handle on it and send a strong message to Islamist groups."
Listen to Premier's Eno Adeogun speaking to April from Christian Solidarity Worldwide:
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