The phrase "were on safe side" can be replaced with a variety of synonyms to express a similar idea. One such synonym is "took precautions," which suggests a level of foresight and planning to avoid potential risks or negative outcomes. Another option is to say someone "played it safe," which conveys a sense of caution and reluctance towards taking unnecessary risks. Additionally, you could use the phrase "erred on the side of caution," which emphasizes a preference for safety over potential gains or benefits. Ultimately, these synonyms all convey a similar message that someone acted responsibly and avoided unnecessary risks or danger.