From data collection to decision making, the life cycle of data often involves many steps of integration, manipulation, and analysis. To be able to provide end-to-end support for the full data life cycle, today's data management and decision making systems increasingly combine operations for data manipulation, integration as well as data analysis. Tensor-relational model (TRM) is a framework proposed to support both relational algebraic operations (for data manipulation and integration) and tensor algebraic operations (for data analysis). In this paper, we consider joint processing of relational algebraic and tensor analysis operations. In particular, we focus on data processing workflows that involve data integration from multiple sources (through unions) and tensor decomposition tasks. While, in traditional relational algebra, the costliest operation is known to be the join, in a framework that provides both relational and tensor operations, tensor decomposition tends to be the computationally costliest operation. Therefore, it is most critical to reduce the cost of the tensor decomposition task by manipulating the data processing workflow in a way that reduces the cost of the tensor decomposition step. Therefore, in this paper, we consider data processing workflows involving tensor decomposition and union operations and we propose a novel scheme for pushing down the tensor decompositions over the union operations to reduce the overall data processing times and to promote reuse of materialized tensor decomposition results. Experimental results confirm the efficiency and effectiveness of the proposed scheme.