No, the Product Owner shouldn't be defining the execution of work during a Sprint.
At the Sprint Planning event, the Product Owner and Developers collaborate to craft a Sprint Goal, select Product Backlog Items for development, and the Developers create an initial plan for achieving the Sprint Goal and delivering the work. These three elements are the Sprint Backlog for the Sprint.
The Developers are accountable for the Sprint Backlog. The plan is created "by and for the Developers". Although the Product Owner is involved in crafting the Sprint Goal and influences the selected Product Backlog Items based on ordering the Product Backlog, the Developers select the work, create the plan, and revise the plan at the Daily Scrum (and more frequently, if necessary).
If the Product Owner is exercising control over the Sprint Backlog and the daily work of the Developers, that could indicate micromanaging and perhaps a lack of trust. It also indicates that the team is not self-organizing and self-managing.