A characterization of the standard Reeb flow

Among the topological conjugacy classes of the continuous flows $\{\phi^t\}$ whose orbit foliations are the planar Reeb foliation, there is one class called the standard Reeb flow. We show that $\{\phi^t\}$ is conjugate to the standard Reeb flow if and only if $\{\phi^t\}$ is conjugate to $\{\phi^{\lambda t}\}$ for any $\lambda>0$.